250 words, no more than 500
· Focus on what you learned that made an impression, what may have surprised you, and what you found particularly beneficial and why. Specifically:
· What did you find that was really useful, or that challenged your thinking?
· What are you still mulling over?
· Was there anything that you may take back to your classroom?
· Is there anything you would like to have clarified?
Your Weekly Reflection will be graded on the following criteria for a total of 5 points:
· Reflection is written in a clear and concise manner, making meaningful connections to the investigations & objectives of the week.
· Reflection demonstrates the ability to push beyond the scope of the course, connecting to prior learning or experiences, questioning personal preconceptions or assumptions, and/or defining new modes of thinking.
BELOW ARE LESSON COVERED
· This week's investigations introduce and explore one of the most common distributions (one you may be familiar with): the Normal Distribution. In our explorations of the distribution and its associated curve, we will revisit the question of "What is typical?" and look at the likelihood (probability) that certain observations would occur in a given population with a variable that is normally distributed. We will apply our work with Normal Distributions to briefly explore some big concepts of inferential statistics, including the Central Limit Theorem and Hypothesis Testing. There are a lot of new ideas in this week’s work. This week is more exploratory in nature.
Goals:
· Explore the Empirical Rule
· Become familiar with the normal curve as a mathematical model, its applications and limitations
· Calculate z-scores & explain what they mean
· Use technology to calculate normal probabilities
· Determine the statistical significance of an observed difference in two means
· Use technology to perform a hypothesis test comparing means (z-test) and interpret its meaning
· Use technology to perform a hypothesis test comparing means (t-test) (optional)
· Gather data for Comparative Study Final Project.
·
DoW #5: The SAT & The ACT
Two Common Tests for college admission are the SAT (Scholastic Aptitude Test) and the ACT (American College Test). The scores for these tests are scaled so that they follow a normal distribution.
· The SAT reported that its scores were normally distributed with a mean μ=896 and a standard deviation σ=174
· The ACT reported that its scores were normally distributed with a mean μ=20.6 and a standard deviation σ=5.2.
We have two questions to consider for this week’s DoW:
2. A high school student Bobby takes both of these tests. On the SAT, he achieves a score of 1080. On the ACT, he achieves a score of 30. He cannot decide which score is the better one to send with his college applications.
. Question: Which test score is the stronger score to send to his colleges?
· A hypothetical group called SAT Prep claims that students who take their SAT Preparatory course score higher o.
Module Five Normal Distributions & Hypothesis TestingTop of F.docxroushhsiu
Module Five: Normal Distributions & Hypothesis Testing
Top of Form
Bottom of Form
·
Introduction & Goals
This week's investigations introduce and explore one of the most common distributions (one you may be familiar with): the Normal Distribution. In our explorations of the distribution and its associated curve, we will revisit the question of "What is typical?" and look at the likelihood (probability) that certain observations would occur in a given population with a variable that is normally distributed. We will apply our work with Normal Distributions to briefly explore some big concepts of inferential statistics, including the Central Limit Theorem and Hypothesis Testing. There are a lot of new ideas in this week’s work. This week is more exploratory in nature.
Goals:
· Explore the Empirical Rule
· Become familiar with the normal curve as a mathematical model, its applications and limitations
· Calculate z-scores & explain what they mean
· Use technology to calculate normal probabilities
· Determine the statistical significance of an observed difference in two means
· Use technology to perform a hypothesis test comparing means (z-test) and interpret its meaning
· Use technology to perform a hypothesis test comparing means (t-test) (optional)
· Gather data for Comparative Study Final Project.
·
DoW #5: The SAT & The ACT
Two Common Tests for college admission are the SAT (Scholastic Aptitude Test) and the ACT (American College Test). The scores for these tests are scaled so that they follow a normal distribution.
· The SAT reported that its scores were normally distributed with a mean μ=896 and a standard deviation σ=174
· The ACT reported that its scores were normally distributed with a mean μ=20.6 and a standard deviation σ=5.2.
We have two questions to consider for this week’s DoW:
2. A high school student Bobby takes both of these tests. On the SAT, he achieves a score of 1080. On the ACT, he achieves a score of 30. He cannot decide which score is the better one to send with his college applications.
. Question: Which test score is the stronger score to send to his colleges?
· A hypothetical group called SAT Prep claims that students who take their SAT Preparatory course score higher on the SAT than the general population. To support their claim, they site a study in which a random sample of 50 SAT Prep students had a mean SAT score of 1000. They claim that since this mean is higher than the known mean of 896 for all SAT scores, their program must improve SAT scores.
. Question: Is this difference in the mean scores statistically significant? Does SAT Prep truly improve SAT Scores?
.
Investigation 1: What is Normal?
One reason for gathering data is to see which observations are most likely. For instance, when we looked at the raisin data in DoW #3, we were looking to see what the most likely number of raisins was for each brand of raisins. We cannot ever be certain of the exact number of raisins in a box (because it varies) ...
QuestionWhich of the following data sets is most likel.docxcatheryncouper
Question
Which of the following data sets is most likely to be normally distributed? For other choices, explain why you believe they would not follow a normal distribution.
The hand span (measured from the tip of the thumb to the tip of the extended 5th finger) of a random sample of high school seniors.
The annual salaries of all employees of a large shipping company
The annual salaries of a random sample of 50 CEOs of major companies (25 men and 25 women)
The dates of 100 pennies taken from a cash drawer in a convenience store
Question
Assume than the mean weight of 1 year old girls in the US is normally distributed with a mean value of 9.5 kg and standard deviation of 1.1. Without using a calculator (use the empirical rule 68 %, 95 %, 99%), estimate the percentage of 1 year old girls in the US that meet the following conditions. Draw a sketch and shade the proper region for each problem…
Less than 8.1 kg
Between 7.3 and 11.7 kg.
More than 12.8 kg.
Question
The grades on a marketing research course midterm are normally distributed with a mean (81) and standard deviation (6.3) . Calculate the z score for each of the following exam grades. Draw and label a sketch for each example.
65
83
93
100
Question
The grades on a marketing research course midterm are normally distributed with a mean (81) and standard deviation (6.3) . Calculate the z score for each of the following exam grades. Draw and label a sketch for each example.
65
83
93
100
Question…
What is the relative frequency of observations below 1.18? That is, find the relative frequency of the event Z < 1.18.
z .00 .01 ... .08 .09
0.0 .5000 .5040 ... .5319 .5359
0.1 .5398 .5438 ... .5714 .5753
... ... ... ... ... ...
1.0 .8413 .8438 ... .8599 .8621
1.1 .8643 .8665 ... .8810 8830
1.2 .8849 .8869 ... .8997 .9015
... ... ... ... ... ...
Question
Find the value z such that the event Z > z has relative frequency 0.80.
Question
For borrowers with good credits the mean debt for revolving and installment accounts is $ 15, 015. Assume the standard deviation is $3,540 and that debt amounts are normally distributed.
What is the probability that the debt for a borrower with good credit is more than $ 18,000.
Question
The average stock price for companies making up the S&P 500 is $30, and the standard deviation is $ 8.20. Assume the stock prices are normally distributed.
How high does a stock price have to be to put a company in the top 10 % … ?
Question
The scores on a statewide geometry exam were normally distributed with μ=72 and σ=8. What fraction of test-takers had a grade between 70 and 72 on the exam? Use the cumulative z-table provided below.
z. 00 .01 .02. 03. 04. 05. 06. 07 .08 .09
0.00. 50000 .50400 .50800 .51200 .51600 .51990 .52390 .52790 .53190 .5359
0.10. 53980 .54380 .54780 .55170 .55570 .55960 .56360 .56750 .57140 .5753
0.20. 57930 .58320 .58710 .59100 .59480 .59870 .60260 .60640 .61 ...
As mentioned earlier, the mid-term will have conceptual and quanti.docxfredharris32
As mentioned earlier, the mid-term will have conceptual and quantitative multiple-choice questions. You need to read all 4 chapters and you need to be able to solve problems in all 4 chapters in order to do well in this test.
The following are for review and learning purposes only. I am not indicating that identical or similar problems will be in the test. As I have indicated in the class syllabus, all the exams in this course will have multiple-choice questions and problems.
Suggestion: treat this review set as you would an actual test. Sit down with your one page of notes and your calculator, and give it a try. That way you will know what areas you still need to study.
ADMN 210
Answers to Review for Midterm #1
1) Classify each of the following as nominal, ordinal, interval, or ratio data.
a. The time required to produce each tire on an assembly line – ratio since it is numeric with a valid 0 point meaning “lack of”
b. The number of quarts of milk a family drinks in a month - ratio since it is numeric with a valid 0 point meaning “lack of”
c. The ranking of four machines in your plant after they have been designated as excellent, good, satisfactory, and poor – ordinal since it is ranking data only
d. The telephone area code of clients in the United States – nominal since it is a label
e. The age of each of your employees - ratio since it is numeric with a valid 0 point meaning “lack of”
f. The dollar sales at the local pizza house each month - ratio since it is numeric with a valid 0 point meaning “lack of”
g. An employee’s identification number – nominal since it is a label
h. The response time of an emergency unit - ratio since it is numeric with a valid 0 point meaning “lack of”
2) True or False: The highest level of data measurement is the ratio-level measurement.
True (you can do the most powerful analysis with this kind of data)
3) True or False: Interval- and ratio-level data are also referred to as categorical data.
False (Interval and ratio level data are numeric and therefore quantitative, NOT qualitative….Nominal is qualitative)
4) A small portion or a subset of the population on which data is collected for conducting statistical analysis is called __________.
A sample! A population is the total group, a census IS the population, and a data set can be either a sample or a population.
5) One of the advantages for taking a sample instead of conducting a census is this:
a sample is more accurate than census
a sample is difficult to take
a sample cannot be trusted
a sample can save money when data collection process is destructive
6) Selection of the winning numbers is a lottery is an example of __________.
convenience sampling
random sampling
nonrandom sampling
regulatory sampling
7) A type of random sampling in which the population is divided into non-overlapping subpopulations is called __________.
stratified random sampling
cluster sampling
systematic random sampling
regulatory sampling
8) A ...
InstructionDue Date 6 pm on October 28 (Wed)Part IProbability a.docxdirkrplav
InstructionDue Date: 6 pm on October 28 (Wed)
Part IProbability and Sampling Distributions1.Thinking about probability statements. Probability is measure of how likely an event is to occur. Match one of probabilities that follow with each statement of likelihood given (The probability is usually a more exact measure of likelihood than is the verbal statement.)Answer0 0.01 0.3 0.6 0.99 1(a) This event is impossible. It can never occur.(b) This event is certain. It will occur on every trial.(c) This event is very unlikely, but it will occur once in a while in a long sequence of trials.(d) This event will occur more often that not.2. Spill or Spell? Spell-checking software catches "nonword errors" that result in a string of letters that is not a word, as when "the" is typed as "the." When undergraduates are asked to write a 250-word essay (without spell-checking), the number X of nonword errors has the following distribution:Value of X01234Probability0.10.20.30.30.1(a) Check that this distribution satisfies the two requirements for a legitimate assignment of probabilities to individual outcomes.(b) Write the event "at least one nonword error" in term of X (for example, P(X >3)). What is the probability of this event?(c) Describe the event X ≤ 2 in words. What is its probability? 3. Discrete or continuous? For each exercise listed below, decide whether the random variable described is discrete or continuous and explains the sample space.(a) Choose a student in your class at random. Ask how much time that student spent studying during the past 24 hours.(b) In a test of a new package design, you drop a carton of a dozen eggs from a height of 1 foot and count the number of broken eggs.(c) A nutrition researcher feeds a new diet to a young male white rat. The response variable is the weight (in grams) that the rat gains in 8 weeks.4. Tossing Coins(a) The distribution of the count X of heads in a single coin toss will be as follows. Find the mean number of heads and the variance for a single coin toss.Number of Heads (Xi)01mean:Probability (Pi)0.50.5variance:(b) The distribution of the count X of heads in four tosses of a balanced coin was as follows but some missing probabilities. Fill in the blanks and then find the mean number of heads and the variance for the distribution with assumption that the tosses are independent of each other.Number of Heads (Xi)01234mean:Probability (Pi)0.06250.0625variance:(c) Show that the two results of the means (i.e. single toss and four tosses) are related by the addition rule for means. (d) Show that the two results of the variances (i.e. single toss and four tosses) are related by the addition rule for variances (note: It was assumed that the tosses are independent of each other). 5. Generating a sampling distribution. Let's illustrate the idea of a sampling distribution in the case of a very small sample from a very small .
Instructions and Advice · This assignment consists of six que.docxdirkrplav
Instructions and Advice:
· This assignment consists of six questions. They each have lots of parts but most of them are very short!
· Data for Questions 3 and 6 are in the companion Excel spreadsheet <Asst3_2013_Data.xlsx>.
· Present the parts of your answers in the same order as the questions are asked.
· Do not include any original data in your printed submission.
· Maintain all precision in your calculator or in Excel as you do your multi-step computations. Round off to fewer decimal places only when you write your work and the final answer down to hand in.
· When formatting numbers in Excel, display only as many decimal places as provide decision-making value to the reader.
Question 1 – Interpreting or Misinterpreting Correlation
a) Various factors are associated with the gross domestic product (GDP) of nations. State whether each of the following statements is reasonable or not. If not, explain the blunder.
(i) A correlation of –0.722 shows that there is almost no association between GDP and Infant Mortality Rate.
(ii) There is a correlation of 0.44 between GDP and Continent.
(iii) There is a very strong correlation of 1.22 between Life Expectancy and GDP.
(iv) The correlation between Literacy Rate and GDP was 0.83. This shows that countries wanting to increase their standard of living should invest heavily in education.
b) An article in a business magazine reported that Internet E-commerce has doubled nearly every three years. It then stated that there was a high correlation between sales made on the Internet and year. Do you think this is an appropriate summary? Explain in one sentence.
c) Simpson’s Paradox can occur in regression, when a relationship between variables within groups of observations is reversed if all the data are combined. Here is an example.
Group
X
Y
Group
X
Y
1
1
10.1
2
6
18.3
1
2
8.9
2
7
17.1
1
3
8.9
2
8
16.2
1
4
6.9
2
9
15.1
1
5
6.1
2
10
14.3
(i) Make a scatterplot of the data for Group 1 and add the least squares line. Describe the relationship between Y and X for Group 1. Find the correlation (using Excel).
(ii) Do the same for Group 2.
(iii) Make a scatterplot using all 10 observations and add the least squares line. Find the correlation (using Excel).
(iv) Summarize your findings in one or two sentences.
d) Since 1980, average mortgage interest rates in the U.S. have fluctuated from a low of under 6% to a high of over 14%. Is there a relationship between the amount of money people borrow and the interest rate that’s offered? Here is a scatterplot of Total Mortgages in the U.S. (in millions of 2005 dollars) vs. Interest Rates at various times over the past 26 years. The correlation is -0.84.
(i) Describe the relationship between Total Mortgages and Interest Rate.
(ii) If we standardized both variables, what would the correlation coefficient between the standardized variables be?
(iii) If we were to measure Total Mortgages in thousands of dollars instead of millions of dollars, how would the.
Module Five Normal Distributions & Hypothesis TestingTop of F.docxroushhsiu
Module Five: Normal Distributions & Hypothesis Testing
Top of Form
Bottom of Form
·
Introduction & Goals
This week's investigations introduce and explore one of the most common distributions (one you may be familiar with): the Normal Distribution. In our explorations of the distribution and its associated curve, we will revisit the question of "What is typical?" and look at the likelihood (probability) that certain observations would occur in a given population with a variable that is normally distributed. We will apply our work with Normal Distributions to briefly explore some big concepts of inferential statistics, including the Central Limit Theorem and Hypothesis Testing. There are a lot of new ideas in this week’s work. This week is more exploratory in nature.
Goals:
· Explore the Empirical Rule
· Become familiar with the normal curve as a mathematical model, its applications and limitations
· Calculate z-scores & explain what they mean
· Use technology to calculate normal probabilities
· Determine the statistical significance of an observed difference in two means
· Use technology to perform a hypothesis test comparing means (z-test) and interpret its meaning
· Use technology to perform a hypothesis test comparing means (t-test) (optional)
· Gather data for Comparative Study Final Project.
·
DoW #5: The SAT & The ACT
Two Common Tests for college admission are the SAT (Scholastic Aptitude Test) and the ACT (American College Test). The scores for these tests are scaled so that they follow a normal distribution.
· The SAT reported that its scores were normally distributed with a mean μ=896 and a standard deviation σ=174
· The ACT reported that its scores were normally distributed with a mean μ=20.6 and a standard deviation σ=5.2.
We have two questions to consider for this week’s DoW:
2. A high school student Bobby takes both of these tests. On the SAT, he achieves a score of 1080. On the ACT, he achieves a score of 30. He cannot decide which score is the better one to send with his college applications.
. Question: Which test score is the stronger score to send to his colleges?
· A hypothetical group called SAT Prep claims that students who take their SAT Preparatory course score higher on the SAT than the general population. To support their claim, they site a study in which a random sample of 50 SAT Prep students had a mean SAT score of 1000. They claim that since this mean is higher than the known mean of 896 for all SAT scores, their program must improve SAT scores.
. Question: Is this difference in the mean scores statistically significant? Does SAT Prep truly improve SAT Scores?
.
Investigation 1: What is Normal?
One reason for gathering data is to see which observations are most likely. For instance, when we looked at the raisin data in DoW #3, we were looking to see what the most likely number of raisins was for each brand of raisins. We cannot ever be certain of the exact number of raisins in a box (because it varies) ...
QuestionWhich of the following data sets is most likel.docxcatheryncouper
Question
Which of the following data sets is most likely to be normally distributed? For other choices, explain why you believe they would not follow a normal distribution.
The hand span (measured from the tip of the thumb to the tip of the extended 5th finger) of a random sample of high school seniors.
The annual salaries of all employees of a large shipping company
The annual salaries of a random sample of 50 CEOs of major companies (25 men and 25 women)
The dates of 100 pennies taken from a cash drawer in a convenience store
Question
Assume than the mean weight of 1 year old girls in the US is normally distributed with a mean value of 9.5 kg and standard deviation of 1.1. Without using a calculator (use the empirical rule 68 %, 95 %, 99%), estimate the percentage of 1 year old girls in the US that meet the following conditions. Draw a sketch and shade the proper region for each problem…
Less than 8.1 kg
Between 7.3 and 11.7 kg.
More than 12.8 kg.
Question
The grades on a marketing research course midterm are normally distributed with a mean (81) and standard deviation (6.3) . Calculate the z score for each of the following exam grades. Draw and label a sketch for each example.
65
83
93
100
Question
The grades on a marketing research course midterm are normally distributed with a mean (81) and standard deviation (6.3) . Calculate the z score for each of the following exam grades. Draw and label a sketch for each example.
65
83
93
100
Question…
What is the relative frequency of observations below 1.18? That is, find the relative frequency of the event Z < 1.18.
z .00 .01 ... .08 .09
0.0 .5000 .5040 ... .5319 .5359
0.1 .5398 .5438 ... .5714 .5753
... ... ... ... ... ...
1.0 .8413 .8438 ... .8599 .8621
1.1 .8643 .8665 ... .8810 8830
1.2 .8849 .8869 ... .8997 .9015
... ... ... ... ... ...
Question
Find the value z such that the event Z > z has relative frequency 0.80.
Question
For borrowers with good credits the mean debt for revolving and installment accounts is $ 15, 015. Assume the standard deviation is $3,540 and that debt amounts are normally distributed.
What is the probability that the debt for a borrower with good credit is more than $ 18,000.
Question
The average stock price for companies making up the S&P 500 is $30, and the standard deviation is $ 8.20. Assume the stock prices are normally distributed.
How high does a stock price have to be to put a company in the top 10 % … ?
Question
The scores on a statewide geometry exam were normally distributed with μ=72 and σ=8. What fraction of test-takers had a grade between 70 and 72 on the exam? Use the cumulative z-table provided below.
z. 00 .01 .02. 03. 04. 05. 06. 07 .08 .09
0.00. 50000 .50400 .50800 .51200 .51600 .51990 .52390 .52790 .53190 .5359
0.10. 53980 .54380 .54780 .55170 .55570 .55960 .56360 .56750 .57140 .5753
0.20. 57930 .58320 .58710 .59100 .59480 .59870 .60260 .60640 .61 ...
As mentioned earlier, the mid-term will have conceptual and quanti.docxfredharris32
As mentioned earlier, the mid-term will have conceptual and quantitative multiple-choice questions. You need to read all 4 chapters and you need to be able to solve problems in all 4 chapters in order to do well in this test.
The following are for review and learning purposes only. I am not indicating that identical or similar problems will be in the test. As I have indicated in the class syllabus, all the exams in this course will have multiple-choice questions and problems.
Suggestion: treat this review set as you would an actual test. Sit down with your one page of notes and your calculator, and give it a try. That way you will know what areas you still need to study.
ADMN 210
Answers to Review for Midterm #1
1) Classify each of the following as nominal, ordinal, interval, or ratio data.
a. The time required to produce each tire on an assembly line – ratio since it is numeric with a valid 0 point meaning “lack of”
b. The number of quarts of milk a family drinks in a month - ratio since it is numeric with a valid 0 point meaning “lack of”
c. The ranking of four machines in your plant after they have been designated as excellent, good, satisfactory, and poor – ordinal since it is ranking data only
d. The telephone area code of clients in the United States – nominal since it is a label
e. The age of each of your employees - ratio since it is numeric with a valid 0 point meaning “lack of”
f. The dollar sales at the local pizza house each month - ratio since it is numeric with a valid 0 point meaning “lack of”
g. An employee’s identification number – nominal since it is a label
h. The response time of an emergency unit - ratio since it is numeric with a valid 0 point meaning “lack of”
2) True or False: The highest level of data measurement is the ratio-level measurement.
True (you can do the most powerful analysis with this kind of data)
3) True or False: Interval- and ratio-level data are also referred to as categorical data.
False (Interval and ratio level data are numeric and therefore quantitative, NOT qualitative….Nominal is qualitative)
4) A small portion or a subset of the population on which data is collected for conducting statistical analysis is called __________.
A sample! A population is the total group, a census IS the population, and a data set can be either a sample or a population.
5) One of the advantages for taking a sample instead of conducting a census is this:
a sample is more accurate than census
a sample is difficult to take
a sample cannot be trusted
a sample can save money when data collection process is destructive
6) Selection of the winning numbers is a lottery is an example of __________.
convenience sampling
random sampling
nonrandom sampling
regulatory sampling
7) A type of random sampling in which the population is divided into non-overlapping subpopulations is called __________.
stratified random sampling
cluster sampling
systematic random sampling
regulatory sampling
8) A ...
InstructionDue Date 6 pm on October 28 (Wed)Part IProbability a.docxdirkrplav
InstructionDue Date: 6 pm on October 28 (Wed)
Part IProbability and Sampling Distributions1.Thinking about probability statements. Probability is measure of how likely an event is to occur. Match one of probabilities that follow with each statement of likelihood given (The probability is usually a more exact measure of likelihood than is the verbal statement.)Answer0 0.01 0.3 0.6 0.99 1(a) This event is impossible. It can never occur.(b) This event is certain. It will occur on every trial.(c) This event is very unlikely, but it will occur once in a while in a long sequence of trials.(d) This event will occur more often that not.2. Spill or Spell? Spell-checking software catches "nonword errors" that result in a string of letters that is not a word, as when "the" is typed as "the." When undergraduates are asked to write a 250-word essay (without spell-checking), the number X of nonword errors has the following distribution:Value of X01234Probability0.10.20.30.30.1(a) Check that this distribution satisfies the two requirements for a legitimate assignment of probabilities to individual outcomes.(b) Write the event "at least one nonword error" in term of X (for example, P(X >3)). What is the probability of this event?(c) Describe the event X ≤ 2 in words. What is its probability? 3. Discrete or continuous? For each exercise listed below, decide whether the random variable described is discrete or continuous and explains the sample space.(a) Choose a student in your class at random. Ask how much time that student spent studying during the past 24 hours.(b) In a test of a new package design, you drop a carton of a dozen eggs from a height of 1 foot and count the number of broken eggs.(c) A nutrition researcher feeds a new diet to a young male white rat. The response variable is the weight (in grams) that the rat gains in 8 weeks.4. Tossing Coins(a) The distribution of the count X of heads in a single coin toss will be as follows. Find the mean number of heads and the variance for a single coin toss.Number of Heads (Xi)01mean:Probability (Pi)0.50.5variance:(b) The distribution of the count X of heads in four tosses of a balanced coin was as follows but some missing probabilities. Fill in the blanks and then find the mean number of heads and the variance for the distribution with assumption that the tosses are independent of each other.Number of Heads (Xi)01234mean:Probability (Pi)0.06250.0625variance:(c) Show that the two results of the means (i.e. single toss and four tosses) are related by the addition rule for means. (d) Show that the two results of the variances (i.e. single toss and four tosses) are related by the addition rule for variances (note: It was assumed that the tosses are independent of each other). 5. Generating a sampling distribution. Let's illustrate the idea of a sampling distribution in the case of a very small sample from a very small .
Instructions and Advice · This assignment consists of six que.docxdirkrplav
Instructions and Advice:
· This assignment consists of six questions. They each have lots of parts but most of them are very short!
· Data for Questions 3 and 6 are in the companion Excel spreadsheet <Asst3_2013_Data.xlsx>.
· Present the parts of your answers in the same order as the questions are asked.
· Do not include any original data in your printed submission.
· Maintain all precision in your calculator or in Excel as you do your multi-step computations. Round off to fewer decimal places only when you write your work and the final answer down to hand in.
· When formatting numbers in Excel, display only as many decimal places as provide decision-making value to the reader.
Question 1 – Interpreting or Misinterpreting Correlation
a) Various factors are associated with the gross domestic product (GDP) of nations. State whether each of the following statements is reasonable or not. If not, explain the blunder.
(i) A correlation of –0.722 shows that there is almost no association between GDP and Infant Mortality Rate.
(ii) There is a correlation of 0.44 between GDP and Continent.
(iii) There is a very strong correlation of 1.22 between Life Expectancy and GDP.
(iv) The correlation between Literacy Rate and GDP was 0.83. This shows that countries wanting to increase their standard of living should invest heavily in education.
b) An article in a business magazine reported that Internet E-commerce has doubled nearly every three years. It then stated that there was a high correlation between sales made on the Internet and year. Do you think this is an appropriate summary? Explain in one sentence.
c) Simpson’s Paradox can occur in regression, when a relationship between variables within groups of observations is reversed if all the data are combined. Here is an example.
Group
X
Y
Group
X
Y
1
1
10.1
2
6
18.3
1
2
8.9
2
7
17.1
1
3
8.9
2
8
16.2
1
4
6.9
2
9
15.1
1
5
6.1
2
10
14.3
(i) Make a scatterplot of the data for Group 1 and add the least squares line. Describe the relationship between Y and X for Group 1. Find the correlation (using Excel).
(ii) Do the same for Group 2.
(iii) Make a scatterplot using all 10 observations and add the least squares line. Find the correlation (using Excel).
(iv) Summarize your findings in one or two sentences.
d) Since 1980, average mortgage interest rates in the U.S. have fluctuated from a low of under 6% to a high of over 14%. Is there a relationship between the amount of money people borrow and the interest rate that’s offered? Here is a scatterplot of Total Mortgages in the U.S. (in millions of 2005 dollars) vs. Interest Rates at various times over the past 26 years. The correlation is -0.84.
(i) Describe the relationship between Total Mortgages and Interest Rate.
(ii) If we standardized both variables, what would the correlation coefficient between the standardized variables be?
(iii) If we were to measure Total Mortgages in thousands of dollars instead of millions of dollars, how would the.
35878 Topic Discussion5Number of Pages 1 (Double Spaced).docxrhetttrevannion
35878 Topic: Discussion5
Number of Pages: 1 (Double Spaced)
Number of sources: 1
Writing Style: APA
Type of document: Essay
Academic Level:Master
Category: Psychology
Language Style: English (U.S.)
Order Instructions: Attached
I will attach the instruction
Please follow them carefully
General Business Page 9
Unit 4
Due Wed 12/12
800-1,000 words / these will be turned into slides and added to your key assignment.
Study the following document: Methods for Managing Differences. Assume this communication strategy has been recommended by your employer for mediation when working with potential and existing business clients and partners.
Consider that there are basically two distinct types of cultures. One type is more cooperative, and the other is more competitive. It has been discovered that there are some conflicts occurring between some of the key players who need to come to agreement on specific critical areas of the deal for it to move forward. The top management would really like this deal to happen.
Imagine being in this situation, and create the scenario as you go through the process using the methods approach from above.
· Describe the steps you would take and any considerations along the way.
· How would you use the recommended method when working with individuals who exhibit a generally competitive culture?
· How would you use the recommended method when working with individuals who exhibit a generally cooperative culture?
· Would this cultural factor change the way you apply this method for managing differences? Why or why not? Explain.
Create Section 4 of your Key Assignment presentation: Global Negotiations. Refer to Unit 1 Discussion Board 2 for a description of this section. Submit a draft of your entire presentation for your instructor to review.
Discussion 2: Discuss, elaborate and give example on the topic below. Please use only the reference I attach. Please be careful with grammar and spelling. No running head Please.
Author: Jackson, S.L. (2017). Statistics Plain and Simple (4th ed.): Cengage Learning
Topic
Review this week’s course materials and learning activities, and reflect on your learning so far this week. Respond to one or more of the following prompts in one to two paragraphs:
1. Provide citation and reference to the material(s) you discuss. Describe what you found interesting regarding this topic, and why.
2. Describe how you will apply that learning in your daily life, including your work life.
3. Describe what may be unclear to you, and what you would like to learn.
Reference:
Module 9: The Single-Sample z Test
The z Test: What It Is and What It Does
The Sampling Distribution
The Standard Error of the Mean
Calculations for the One-Tailed z Test
Interpreting the One-Tailed z Test
Calculations for the Two-Tailed z Test
Interpreting the Two-Tailed z Test
Statistical Power
Assumptions and Appropriate Use of the z Test
Confidence Intervals Based on the z Distribution
Review of Key Term.
Ashford 2: - Week 1 - Instructor Guidance
Week Overview:
The following video series: Against All Odds Inside Statistics is helpful if you would like to watch it.
http://www.learner.org/resources/series65.html?pop=yes&pid=3138
For this week, we’ll learn that statistics is the science of collecting, organizing, presenting, analyzing, and interpreting numerical data to assist in making more effective decisions.
In today’s world, numerical information is everywhere. Statistical techniques are used to make decisions that affect our daily lives. The knowledge of statistical methods will help you understand how decisions are made and give you a better understanding of how they affect you. No matter what line of work you select, you will find yourself faced with decisions where an understanding of data analysis is helpful.
The concepts introduced this week include levels of measurement, measurements of center, variations, etc. Normal distribution and calculations are introduced in this week.
Measurements
You should be able to distinguish among the nominal, ordinal, interval, and ratio levels of measurement.
Nominal level - data that is classified into categories and cannot be arranged in any particular order.
EXAMPLES: eye color, gender, religious affiliation.
Ordinal level – data arranged in some order, but the differences between data values cannot be determined or are meaningless.
EXAMPLE: During a taste test of 4 soft drinks, Mellow Yellow was ranked number 1, Sprite number 2, Seven-up number 3, and Orange Crush number 4.
Interval level - similar to the ordinal level, with the additional property that meaningful amounts of differences between data values can be determined. There is no natural zero point.
EXAMPLE: Temperature on the Fahrenheit scale.
Ratio level - the interval level with an inherent zero starting point. Differences and ratios are meaningful for this level of measurement.
EXAMPLES: Monthly income of surgeons, or distance traveled by manufacturer’s representatives per month.
Why do you need to know the level of measurement of a data? This is because the level of measurement of the data dictates the calculations that can be done to summarize and present the data. It also determines the statistical tests that should be performed on the data.
Probability
PROBABILITY is a value between zero and one, inclusive, describing the relative possibility (chance or likelihood) an event will occur.
There are three ways of assigning probability:
1. Classical Probability
This is based on the assumption that the outcomes of an experiment are equally likely.
2. Empirical Probability
The probability of an event happening is the fraction of the time similar events happened in the past.
Example: On February 1, 2003, the Space Shuttle Columbia exploded. This was the second disaster in 113 space missions for NASA. On the basis of this information, what is the probability that a future mission is successfully completed?
Probability of successful flight ...
Dear students get fully solved assignments
Send your semester & Specialization name to our mail id :
help.mbaassignments@gmail.com
or
call us at : 08263069601
Answer the questions in one paragraph 4-5 sentences. · Why did t.docxboyfieldhouse
Answer the questions in one paragraph 4-5 sentences.
· Why did the class collectively sign a blank check? Was this a wise decision; why or why not? we took a decision all the class without hesitation
· What is something that I said individuals should always do; what is it; why wasn't it done this time? Which mitigation strategies were used; what other strategies could have been used/considered? individuals should always participate in one group and take one decision
SAMPLING MEAN:
DEFINITION:
The term sampling mean is a statistical term used to describe the properties of statistical distributions. In statistical terms, the sample meanfrom a group of observations is an estimate of the population mean. Given a sample of size n, consider n independent random variables X1, X2... Xn, each corresponding to one randomly selected observation. Each of these variables has the distribution of the population, with mean and standard deviation. The sample mean is defined to be
WHAT IT IS USED FOR:
It is also used to measure central tendency of the numbers in a database. It can also be said that it is nothing more than a balance point between the number and the low numbers.
HOW TO CALCULATE IT:
To calculate this, just add up all the numbers, then divide by how many numbers there are.
Example: what is the mean of 2, 7, and 9?
Add the numbers: 2 + 7 + 9 = 18
Divide by how many numbers (i.e., we added 3 numbers): 18 ÷ 3 = 6
So the Mean is 6
SAMPLE VARIANCE:
DEFINITION:
The sample variance, s2, is used to calculate how varied a sample is. A sample is a select number of items taken from a population. For example, if you are measuring American people’s weights, it wouldn’t be feasible (from either a time or a monetary standpoint) for you to measure the weights of every person in the population. The solution is to take a sample of the population, say 1000 people, and use that sample size to estimate the actual weights of the whole population.
WHAT IT IS USED FOR:
The sample variance helps you to figure out the spread out in the data you have collected or are going to analyze. In statistical terminology, it can be defined as the average of the squared differences from the mean.
HOW TO CALCULATE IT:
Given below are steps of how a sample variance is calculated:
· Determine the mean
· Then for each number: subtract the Mean and square the result
· Then work out the mean of those squared differences.
To work out the mean, add up all the values then divide by the number of data points.
First add up all the values from the previous step.
But how do we say "add them all up" in mathematics? We use the Roman letter Sigma: Σ
The handy Sigma Notation says to sum up as many terms as we want.
· Next we need to divide by the number of data points, which is simply done by multiplying by "1/N":
Statistically it can be stated by the following:
·
· This value is the variance
EXAMPLE:
Sam has 20 Rose Bushes.
The number of flowers on each b.
I need a 7 pg research essay on the following Select a real o.docxeugeniadean34240
I need a 7 pg research essay on the following:
Select a real or hypothetical crisis, such as a natural disaster (hurricane, tornado, flooding, or earthquake), a catastrophic building failure, or an act of terrorism.
Discuss resource management based on ethical approaches used during crisis management.
Consider issues such as patient triage or current as well as incoming patients, supply, and personnel availability.
Discuss and develop an authoritative chain of command for crisis management.
Include such responsibilities as Incident Commander, Communications Officer, and other members of the chain of command for the incident.
Discuss the importance and implementation of community communication, involvement, and coordination.
Discuss the necessary policies for personnel management and safety.
Include provisions for lock-down status and family communication abilities.
Outline the steps for supply chain management, both for personnel and the supplies needed to provide care.
.
I need a 4-5 APA formatted paper with references that is clearly wri.docxeugeniadean34240
I need a 4-5 APA formatted paper with references that is clearly written and includes the following:
The attendance of an AA meeting. Describe the meeting's atmosphere, the participants and their appearances, details on the group discussion, engagement, timeframe, the pros and cons of the meeting, and other helpful information.
.
More Related Content
Similar to 250 words, no more than 500· Focus on what you learned that made.docx
35878 Topic Discussion5Number of Pages 1 (Double Spaced).docxrhetttrevannion
35878 Topic: Discussion5
Number of Pages: 1 (Double Spaced)
Number of sources: 1
Writing Style: APA
Type of document: Essay
Academic Level:Master
Category: Psychology
Language Style: English (U.S.)
Order Instructions: Attached
I will attach the instruction
Please follow them carefully
General Business Page 9
Unit 4
Due Wed 12/12
800-1,000 words / these will be turned into slides and added to your key assignment.
Study the following document: Methods for Managing Differences. Assume this communication strategy has been recommended by your employer for mediation when working with potential and existing business clients and partners.
Consider that there are basically two distinct types of cultures. One type is more cooperative, and the other is more competitive. It has been discovered that there are some conflicts occurring between some of the key players who need to come to agreement on specific critical areas of the deal for it to move forward. The top management would really like this deal to happen.
Imagine being in this situation, and create the scenario as you go through the process using the methods approach from above.
· Describe the steps you would take and any considerations along the way.
· How would you use the recommended method when working with individuals who exhibit a generally competitive culture?
· How would you use the recommended method when working with individuals who exhibit a generally cooperative culture?
· Would this cultural factor change the way you apply this method for managing differences? Why or why not? Explain.
Create Section 4 of your Key Assignment presentation: Global Negotiations. Refer to Unit 1 Discussion Board 2 for a description of this section. Submit a draft of your entire presentation for your instructor to review.
Discussion 2: Discuss, elaborate and give example on the topic below. Please use only the reference I attach. Please be careful with grammar and spelling. No running head Please.
Author: Jackson, S.L. (2017). Statistics Plain and Simple (4th ed.): Cengage Learning
Topic
Review this week’s course materials and learning activities, and reflect on your learning so far this week. Respond to one or more of the following prompts in one to two paragraphs:
1. Provide citation and reference to the material(s) you discuss. Describe what you found interesting regarding this topic, and why.
2. Describe how you will apply that learning in your daily life, including your work life.
3. Describe what may be unclear to you, and what you would like to learn.
Reference:
Module 9: The Single-Sample z Test
The z Test: What It Is and What It Does
The Sampling Distribution
The Standard Error of the Mean
Calculations for the One-Tailed z Test
Interpreting the One-Tailed z Test
Calculations for the Two-Tailed z Test
Interpreting the Two-Tailed z Test
Statistical Power
Assumptions and Appropriate Use of the z Test
Confidence Intervals Based on the z Distribution
Review of Key Term.
Ashford 2: - Week 1 - Instructor Guidance
Week Overview:
The following video series: Against All Odds Inside Statistics is helpful if you would like to watch it.
http://www.learner.org/resources/series65.html?pop=yes&pid=3138
For this week, we’ll learn that statistics is the science of collecting, organizing, presenting, analyzing, and interpreting numerical data to assist in making more effective decisions.
In today’s world, numerical information is everywhere. Statistical techniques are used to make decisions that affect our daily lives. The knowledge of statistical methods will help you understand how decisions are made and give you a better understanding of how they affect you. No matter what line of work you select, you will find yourself faced with decisions where an understanding of data analysis is helpful.
The concepts introduced this week include levels of measurement, measurements of center, variations, etc. Normal distribution and calculations are introduced in this week.
Measurements
You should be able to distinguish among the nominal, ordinal, interval, and ratio levels of measurement.
Nominal level - data that is classified into categories and cannot be arranged in any particular order.
EXAMPLES: eye color, gender, religious affiliation.
Ordinal level – data arranged in some order, but the differences between data values cannot be determined or are meaningless.
EXAMPLE: During a taste test of 4 soft drinks, Mellow Yellow was ranked number 1, Sprite number 2, Seven-up number 3, and Orange Crush number 4.
Interval level - similar to the ordinal level, with the additional property that meaningful amounts of differences between data values can be determined. There is no natural zero point.
EXAMPLE: Temperature on the Fahrenheit scale.
Ratio level - the interval level with an inherent zero starting point. Differences and ratios are meaningful for this level of measurement.
EXAMPLES: Monthly income of surgeons, or distance traveled by manufacturer’s representatives per month.
Why do you need to know the level of measurement of a data? This is because the level of measurement of the data dictates the calculations that can be done to summarize and present the data. It also determines the statistical tests that should be performed on the data.
Probability
PROBABILITY is a value between zero and one, inclusive, describing the relative possibility (chance or likelihood) an event will occur.
There are three ways of assigning probability:
1. Classical Probability
This is based on the assumption that the outcomes of an experiment are equally likely.
2. Empirical Probability
The probability of an event happening is the fraction of the time similar events happened in the past.
Example: On February 1, 2003, the Space Shuttle Columbia exploded. This was the second disaster in 113 space missions for NASA. On the basis of this information, what is the probability that a future mission is successfully completed?
Probability of successful flight ...
Dear students get fully solved assignments
Send your semester & Specialization name to our mail id :
help.mbaassignments@gmail.com
or
call us at : 08263069601
Answer the questions in one paragraph 4-5 sentences. · Why did t.docxboyfieldhouse
Answer the questions in one paragraph 4-5 sentences.
· Why did the class collectively sign a blank check? Was this a wise decision; why or why not? we took a decision all the class without hesitation
· What is something that I said individuals should always do; what is it; why wasn't it done this time? Which mitigation strategies were used; what other strategies could have been used/considered? individuals should always participate in one group and take one decision
SAMPLING MEAN:
DEFINITION:
The term sampling mean is a statistical term used to describe the properties of statistical distributions. In statistical terms, the sample meanfrom a group of observations is an estimate of the population mean. Given a sample of size n, consider n independent random variables X1, X2... Xn, each corresponding to one randomly selected observation. Each of these variables has the distribution of the population, with mean and standard deviation. The sample mean is defined to be
WHAT IT IS USED FOR:
It is also used to measure central tendency of the numbers in a database. It can also be said that it is nothing more than a balance point between the number and the low numbers.
HOW TO CALCULATE IT:
To calculate this, just add up all the numbers, then divide by how many numbers there are.
Example: what is the mean of 2, 7, and 9?
Add the numbers: 2 + 7 + 9 = 18
Divide by how many numbers (i.e., we added 3 numbers): 18 ÷ 3 = 6
So the Mean is 6
SAMPLE VARIANCE:
DEFINITION:
The sample variance, s2, is used to calculate how varied a sample is. A sample is a select number of items taken from a population. For example, if you are measuring American people’s weights, it wouldn’t be feasible (from either a time or a monetary standpoint) for you to measure the weights of every person in the population. The solution is to take a sample of the population, say 1000 people, and use that sample size to estimate the actual weights of the whole population.
WHAT IT IS USED FOR:
The sample variance helps you to figure out the spread out in the data you have collected or are going to analyze. In statistical terminology, it can be defined as the average of the squared differences from the mean.
HOW TO CALCULATE IT:
Given below are steps of how a sample variance is calculated:
· Determine the mean
· Then for each number: subtract the Mean and square the result
· Then work out the mean of those squared differences.
To work out the mean, add up all the values then divide by the number of data points.
First add up all the values from the previous step.
But how do we say "add them all up" in mathematics? We use the Roman letter Sigma: Σ
The handy Sigma Notation says to sum up as many terms as we want.
· Next we need to divide by the number of data points, which is simply done by multiplying by "1/N":
Statistically it can be stated by the following:
·
· This value is the variance
EXAMPLE:
Sam has 20 Rose Bushes.
The number of flowers on each b.
I need a 7 pg research essay on the following Select a real o.docxeugeniadean34240
I need a 7 pg research essay on the following:
Select a real or hypothetical crisis, such as a natural disaster (hurricane, tornado, flooding, or earthquake), a catastrophic building failure, or an act of terrorism.
Discuss resource management based on ethical approaches used during crisis management.
Consider issues such as patient triage or current as well as incoming patients, supply, and personnel availability.
Discuss and develop an authoritative chain of command for crisis management.
Include such responsibilities as Incident Commander, Communications Officer, and other members of the chain of command for the incident.
Discuss the importance and implementation of community communication, involvement, and coordination.
Discuss the necessary policies for personnel management and safety.
Include provisions for lock-down status and family communication abilities.
Outline the steps for supply chain management, both for personnel and the supplies needed to provide care.
.
I need a 4-5 APA formatted paper with references that is clearly wri.docxeugeniadean34240
I need a 4-5 APA formatted paper with references that is clearly written and includes the following:
The attendance of an AA meeting. Describe the meeting's atmosphere, the participants and their appearances, details on the group discussion, engagement, timeframe, the pros and cons of the meeting, and other helpful information.
.
I need a 3 page research paper on Title Addictive being youn.docxeugeniadean34240
I need a 3 page research paper on
Title:
Addictive being young and older on Social Media, why activities outdoors can prevent addiction
In the attached zip file, I have provided 10 journals that you need to use for this research paper.
In the word doc, I have shared the topic and sub-topics that you have to use. And it also has guidelines from the teacher for this paper.
Due on Saturday, 13th March 4PM PST
.
I need a 3 page double-spaced 12-point paper on Immunotherapy. the i.docxeugeniadean34240
I need a 3 page double-spaced 12-point paper on Immunotherapy. the information must be obtained from at least three original research articles, not from blogs news, etc.. must have work cited page. should include Introductory, Body(divided into smaller sections), Summary or Conclusion, followed by the references. I need this done by April 30, 2021 10:30pm Eastern Daylight Time
.
I need a 2500 word essay on the 1st Battalion 7th Cavalry Regiment. .docxeugeniadean34240
I need a 2500 word essay on the 1st Battalion 7th Cavalry Regiment. The paper needs to start with training the unit before deploying to Vietnam. How they perfected thier new traininf with helicopters. It needs to talk about both LTC Hal Moore and CSM Basil Plumbly. It needs to talk about how the unit remained resilient and how they over came racism and the battle in Vietnam.
.
I need a 200-word paper that answers the following questions:D.docxeugeniadean34240
I need a 200-word paper that answers the following questions:
Describe the term Enterprise Architecture (EA), what it means, how it can be used, and the core elements on EA. What are the core elements within EA.?
Now compare EA to Information Systems – are there any similarities, any differences?
.
i need a 2 page essay on LA crimes as it pertains to Rape you will h.docxeugeniadean34240
i need a 2 page essay on LA crimes as it pertains to Rape you will have to response to the data regarding observed disparities in offenders vs. incarcertaion of Rape offense in Louisiana. also you will have to included a critical and well reasoned to the incarceration rate in Louisiana as a whole vs. the US.
.
I need a 1 page professional bio. My cover letter and resume i.docxeugeniadean34240
I need a 1 page professional bio.
My cover letter and resume is attached.
As an experienced and motivated professional with exceptional leadership and interpersonal abilities, I am prepared to significantly contribute to your organization’s goals in this role.
My background lies in workforce and economic development, managing operations, teams, conflict resolution, and processes to propel revenue increases while realizing enhanced corporate success and productivity. From establishing and implementing visionary business strategies to driving employees to achieve peak performance levels, I excel at directing strategic enhancements to outperform open objectives while communicating openly and effectively with staff and management teams.
Highlights of my experience include the following:
Ø Excelling as the Manager of the workforce development team with the Shelby County Alternative Schools for the past 10 years, federal grant management, identifying employment opportunities for youth and adult offenders, educating and supporting clients through vocational training initiatives, evaluating client work interests and aptitudes, and connecting clients with eligible and appropriate employment programs.
Ø Assisting program participants in identifying anger, recognizing aggressive behavior triggers, and learning tension and anger management techniques.
Ø Coaching and mentoring staff to ensure outstanding job performances and maximum program effectiveness. (virtual and face-to-face)
Ø Scheduling and coordinating opportunities for training, recreation, and leisure activities tailored to participants ‘preferences and age-appropriateness
Ø Encouraging an atmosphere supportive of constructive feedback and performance evaluation/improvement
Ø Adept at establishing goals and driving achievement through education, training, communication, and resource utilization
Ø Maintaining detailed records and reports to document participant progress and status
Ø Demonstrating solid time management, interpersonal, and organizational skills, as well as Microsoft Office proficiency.
Ø Compiling and analyzing client data obtained through records, tests, interviews, and other professional sources, determining clients’ suitability for various job opportunities and vocational training programs
Ø Facilitating and leading both individual and group orientation sessions and educating participants on requirements for participation in agency- sponsored programs
Ø Establishing solid and trusting relationships through exceptional relationship-building skills; utilizing solid communication and interpersonal abilities to secure employer and client trust
My proven dedication to optimizing workforce development and employment success through my expert knowledge of learning, development, and conflict resolution strategies will contribute immensely to the success of your-team.
.
I need 100 words response for this two discussion forum1 discu.docxeugeniadean34240
I need 100 words response for this two discussion forum
1 discussion
Colin Kaepernick comes to mind as I speak of racial differences, principles and morals. Colin Kaepernick, when he chose to go beyond the usual practice, effectively gave up his dream. Colin Kaepernick, the American football player who started the National Anthem "take knee" campaign against racial violence against African American and other races. Business ethics is the study of what constitutes right or wrong, good or bad human conduct in a business environment. The introduction of universal ethical principles to particular practical problems in the modern environment, such as dishonesty in ads, bullying, etc., is intended to assess what is "valid" behavior; i.e. what is considered appropriate or "right" conduct in line with universal ethical values (Christie et al, 2003).
I served with a social-service organization in 2013. Within this unique setting, I have been forced to interact alongside a variety of communities and faiths. Each of the SNAP entitlements (Food stamps) is dependent on family revenue and wealth. There was, however, a misconception and theory circulated inside the department that African American culture is lazy and that many of them do not want to function and want to rely on the government for assistance. I know that the theory and the story arose from the deep-rooted fear of the Slavery. Under which racial violence persists and so other groups are still competing and killing each other.
At another agency I worked for I worked with youth directly in a foster care setting. I am African American, and the rest of the children I represent are Hispanic / Latino. I note that when I'm out in the city with my Hispanic / Latino clientele, I typically get a number of stares from various cultures. One of my four-year-old children sometimes holds a temper tantrum to get what she needs from her mother. She decided to have one of these tantrums with me when we were in the grocery shop. I dismissed her actions, and there was a Hispanic lady who came up to me with a really unpleasant attitude, telling me to know what I was doing to the girl. I dismissed her and proceeded to focus on the actions of my client. I assume that she just got embroiled in this scenario because I mistreated this Hispanic child in her opinion, even though I gave her my badge for work. Anything I did with the child was in compliance with the Agency's rules and practices, even when I was being confronted by a consumer in the shop. It's really difficult to deal with babies, youth and even the elderly, so you also have to make sure that you perform it according to policies and procedures. Mandatory ethics was enforced to safeguard the employees who work for the specific organization and even the clients. Professionals are required to recognize and live by their Code of Ethics. Practitioners will need to demonstrate awareness regarding the adaptation of their codes to different cultures (Weber 20004).
I need 200 words response for each discussion post.Guided Respon.docxeugeniadean34240
I need 200 words response for each discussion post.
Guided Response: Respond to at least two of your classmates’ postings. Support your initial and subsequent posts by citing at least two scholarly and peer-reviewed sources in addition to the course text. The Scholarly, Peer-Reviewed, and Other Credible Sources (Links to an external site.) table offers additional guidance on appropriate source types.
Forum 1)One psychosocial issue that could cause a serious issue in the school setting to me would be Bullying. Bullying can scare a person’s ability to feel be ant to bully and be mean to someone because they may act different or look different to them, beautiful, safe, and secure about who they are, and be lasting ongoing issue that will last forever by making them feel insecure, and not wanted along while feeling like no one cares about them. Bullying is a form of abuse, aggressiveness, coercion, force. There are other things that bullies do to feel like they are important or better than everyone else, like be dominated, intimidating, or threatening. “Bullying in schools, particularly bias-based bullying, is an important issue for many reasons, but chief among them include evidence that victims being bullied experience both short and long term consequences, including poor school performance, depression, and increased health problems” (Martin, M. E. (2018).
I believe that the services of all three would be required because the bully would be evaluated three different times on his behavior and other things that no one may know about. Each of them has their own specialty that would fit working with the bully and being able to determine what is the issue or problem that makes the bully act out of character the way he or she does.
“An analysis of this phenomenon in schools, according to different authors [1,7.8, reveals that children involved in bullying behavior can play different roles; (a) aggressors/intimidators; (b) victim; (c) aggressors who are also victims and (d) passive observers. These observers are neither directly involved as aggressors nor as victims. As such, they can play a number of different roles: they can defend the victims, thus reducing this type of behavior; they can support the aggressors, actively reinforcing intimidation; children who merely observe are neutral or indifferent”. (www.ncbi.nim.nih.gov) (Links to an external site.) . There should something put into place that will stop individuals with aggressive behavior to stop bullying other individuals who just want to be themselves and live their lives. It leads to most children feeling depressed and wanting to end their lives because of it, and it happens in our society today children ending their lives because they are being targeted by bullies. Rules should also be put into place for the bullies to let them know what will happen if they continue to bully others.
REFERENCES:
Martin, M. E. (2018). Introduction to human services: Through the eyes of practice settings .
I need 3 pages discussion for an intersection (Attached image).docxeugeniadean34240
I need 3 pages discussion for an intersection (Attached image)
North Harbor Drive and Harbor Island Drive intersection, San Diego CA 92111 US
Please address the following:
a. Right of Way Issues
b. Utility Relocation
c. Air Quality Conformity
d. Title VI Considerations
e. Visual / Landscape Considerations
f. Required Permits
g. Stormwater Management
h. Cultural Resources
i. Risk Management Plan
j. Transportation Management Plan (TMP)
k. Transit Services
If you think any other better ideas, please address them as well.
University Level
Please no plagiarism
I also attached an example, you can follow it to get ideas to write about
.
I need 1page write up on Hypothesis & Methods Proposal,Due on .docxeugeniadean34240
I need 1page write up on Hypothesis & Methods Proposal,
Due on 3rd Feb 7PM PST
Please see attached doc for details on title, notes and questions to be answered.
Please cite everything, You might need the previous APA paper (attached image), but not sure. so please review
.
I need 2-3 pages written about the sieve of Eratosthenes. Starti.docxeugeniadean34240
I need 2-3 pages written about the sieve of Eratosthenes. Starting from the Eratosthenes-legendre sieve going to Eratosthenes general sieve, while giving some detailed formulas and explanations for each, using some lemma and examples. And finishing with some applications.
The work has to be authentic and original (not copied), with the references stated where its used on the paper and at the end
.
I need 120 words for each question. Please ensure to post individual.docxeugeniadean34240
I need 120 words for each question. Please ensure to post individual reference with each question
Unit 1
Q 1;
Identify two organizational structures used in health care. What are the central characteristics of each? To what extent is bureaucracy necessary in health care organizations? Explain.
Q 2;
How does a doctorally prepared nurse work across and between levels of an organization? What are the challenges and/or rewards to be gained? Does one outweigh the other?
Resources
Delmatoff, J., & Lazarus, I. R. (2014). The most effective leadership style for the new landscape of healthcare.
Journal of Healthcare Management, 59
(4), 245-249. URL:
https://lopes.idm.oclc.org/login?url=http://search.ebscohost.com.lopes.idm.oclc.org/login.aspx?direct=true&db=a9h&AN=97206195&site=ehost-live&scope=site
Arbab Kash, B., Spaulding, A., Johnson, C. E., & Gamm, L. (2014). Success factors for strategic change initiatives: A qualitative study of healthcare administrators' perspectives.
Journal of Healthcare Management, 59
(1), 65-81. URL:
https://lopes.idm.oclc.org/login?url=http://search.ebscohost.com.lopes.idm.oclc.org/login.aspx?direct=true&db=a9h&AN=94059299&site=ehost-live&scope=site
Kritsonis, A. (2004/2005). Comparison of change theories.
International Journal of Scholarly Academic Intellectual Diversity, 8
(1) 1-7. URL:
http://qiroadmap.org/?wpfb_dl=12
Suter, E., Goldman, J., Martimianakis, T., Chatalalsingh, C., Dematteo, D. J., & Reeves, S. (2013). The use of systems and organizational theories in the interprofessional field: Findings from a scoping review.
Journal of Interprofessional Care, 27
(1), 57-64. doi:10.3109/13561820.2012.739670 URL:
https://lopes.idm.oclc.org/login?url=http://search.ebscohost.com.lopes.idm.oclc.org/login.aspx?direct=true&db=a9h&AN=84423842&site=ehost-live&scope=site
Narayana, E. A. (1992). Bureaucratization of non-governmental organizations: An analysis of employees' perceptions and attitudes.
Public Administration and Development, 12
(2), 123-137. URL:
https://lopes.idm.oclc.org/login?url=http://search.proquest.com.lopes.idm.oclc.org/docview/194674953?accountid=7374
Klemsdal, L. (2013). From bureaucracy to learning organization: Critical minimum specification design as space for sensemaking.
Systemic Practice & Action Research
,
26
(1), 39-52. doi:10.1007/s11213-012-9267-3 URL:
https://lopes.idm.oclc.org/login?url=http://search.ebscohost.com/login.aspx?direct=true&db=bth&AN=84739308&site=ehost-live&scope=site
Unit 2
Q 1:
What are three payment structures used in the health care industry across the care continuum? How are they similar? How are they different? Is there a single problem that transverses all three of the identified payment structures? Explain.
Q 2:
Identify a significant problem with one of the three payment structures used in the health care industry across the care continuum (from DQ 1) and propose a solution from one of the other two payment structures.
Resources
.
I need 10-12 slides Presentation with detailed speaker notes. Instru.docxeugeniadean34240
I need 10-12 slides Presentation with detailed speaker notes. Instruction is given below. It is a Religion Class. No Plagiarism Please. Due in 24 hours.
Wk 3 - Christianity Presentation
Create
a 10- to 12-slide presentation comparing
2
of the following branches of Christianity:
Catholic
Orthodox
Protestant
Include
a brief history of the 2 religious traditions and a comparison of their approaches to the Bible. Some concepts to include are:
Examples of art
Central symbols of the faith
Rituals and core beliefs
Ethics role in the faith
You might consider visiting one or more of these churches in person or exploring church websites to add to your own experiences.
.
I N N O V A T I O N N E T W O R K , I N C . www.innone.docxeugeniadean34240
I N N O V A T I O N N E T W O R K , I N C .
www.innonet.org • [email protected]
L o g i c M o d e l W o r k b o o k
I N N O V A T I O N N E T W O R K , I N C .
www.innonet.org • [email protected]
L o g i c M o d e l W o r k b o o k
T a b l e o f C o n t e n t s
P a g e
Introduction - How to Use this Workbook .....................................................................2
Before You Begin .................................................................................................................3
Developing a Logic Model .................................................................................................4
Purposes of a Logic Model ............................................................................................... 5
The Logic Model’s Role in Evaluation ............................................................................ 6
Logic Model Components – Step by Step ....................................................................... 6
Problem Statement: What problem does your program address? ......................... 6
Goal: What is the overall purpose of your program? .............................................. 7
Rationale and Assumptions: What are some implicit underlying dynamics? ....8
Resources: What do you have to work with? ......................................................... 9
Activities: What will you do with your resources? ................................................ 11
Outputs: What are the tangible products of your activities? ................................. 13
Outcomes: What changes do you expect to occur as a result of your work?.......... 14
Outcomes Chain ....................................................................................... 16
Outcomes vs. Outputs ............................................................................. 17
Logic Model Review ...........................................................................................................18
Appendix A: Logic Model Template
Appendix B: Worksheet: Developing an Outcomes Chain
Logic Model Workbook
Page 2
I N N O V A T I O N N E T W O R K , I N C .
www.innonet.org • [email protected]
I n t r o d u c t i o n - H o w t o U s e t h i s W o r k b o o k
Welcome to Innovation Network’s Logic Model Workbook. A logic model is a commonly-used
tool to clarify and depict a program within an organization. You may have heard it described as
a logical framework, theory of change, or program matrix—but the purpose is usually the same:
to graphically depict your program, initiative, project or even the sum total of all of your
organization’s work. It also serves as a
foundation for program planning and
evaluation.
This workbook is a do-it-yourself guide to
the concepts and use of the logic model. It
describes the steps necessary for you to
create logic models fo.
I like to tie my learning to Biblical Principles. On Virtuous Le.docxeugeniadean34240
I like to tie my learning to Biblical Principles. On Virtuous Leadership, I think about what leader in the Bible do I know that stands out as a virtuous leader. Although there are many, one that stands out to me is Nehemiah. Nehemiah's brother and others said that they had been to Jerusalem and the Wall has been broken down, and the gates were burned. Nehemiah listened and took this news personally as if he was the wounded party. In other words, it broke his heart to hear this news.
He then took personal responsibility, prayed, and asked God to forgive him and his people for not obeying his commands. Then he took personal action, and at great danger to himself, he appeared before the King sad - remember that no King wants a sad cupbearer. When the King saw how sad Nehemiah was, he asked him why, and Nehemiah explained the state of his city walls and asked permission to go and fix them. He went and fixed the walls. He got involved in the work as a servant leader and getting the people what they needed. They had a city again with walls and a gate, and most importantly, they had protection!
We can see in this story that a servant leader is someone who takes personal responsibility for what has gone wrong and sets out to fix it, but not only does he/she fix the problem, the servant leader gets involved in the work and works alongside his workers to get the job done right. By doing so, the servant leader demonstrates his care for his workers and organization.
Share a story of a servant leader either in the Bible or someone you know.
.
I just want one paragraph.!!C.W.Mills described ‘sociological im.docxeugeniadean34240
I just want one paragraph.!!
C.W.Mills described ‘sociological imagination’ as an ability to understand “the intersection of one's own biography and other biographies with history and the present social structure you find yourself and others in.” In short, it is the ability to understand the private in public terms. Essentially, Mills is describing an ability to discern patterns in social events and view personal experiences in light of those patterns. To highlight that, he uses two terms – “the personal troubles of milieu” and “the public issues of social structure.” ‘Troubles’ happen to us as individuals, and are a private matter of individual choices and biography. ‘Issues’ are public matters that transcend the individual, and have to do with societal structures and processes.
Here is the Question!!!
1- For this discussion, I want you to select one of the following health/medical issues, and offer a thoughtful reflection on it as both a hypothetical ‘personal trouble’ and a ‘public issue.’
- ADHD; obesity; eating disorder; infertility; Alzheimer’s disease; COVID.
.
i just need serious help answering the question. I have answered mos.docxeugeniadean34240
i just need serious help answering the question. I have answered most of them but the following posted questions are giving me problem.
# 1.1
(1 pts.) In the textbook case, what information led Dr. Tobin to conclude that Shaun Boyden's sexual attraction to children was not a passing fancy? '
A) the fact that he reported having the urges since adolescence
B) the fact that his wife was unaware of his problem
C) the fact that he was never caught in the past
D) the fact that he had a relatively normal sexual development
# 1.2
(1 pts.) Charlie has opted to have psychosurgery performed in order to change his pedophilic patterns. Which of the following procedures will Charlie have done?
A) prefrontal lobotomy
B) hypothalamotomy
C) castration
D) vasectomy
# 1.3
(1 pts.) Dr. Walters is instructing Harry to imagine that he has just "flashed" his genitals at an unsuspecting woman on the street. After the woman responds in horror, Harry is to imagine that all of his closest friends jump out of a nearby alley and start laughing at him. Dr. Walters is using the technique known as
A) systematic desensitization.
B) cognitive restructuring.
C) covert conditioning.
D) behavior modification.
# 1.4
(1 pts.) Who is most likely to be the target of a frotteurist's desires?
A) a person from work
B) a life-long friend
C) a shopper at the mall
D) a close relative
# 1.9
(1 pts.) Based on the information presented in the textbook case, Shaun Boyden might be considered a ______ since he had a normal history of sexual development and interests.
A) child rapist
B) preference molester
C) situational molester
D) generalized molester
# 1.12
(1 pts.) Joe becomes sexually aroused when he views sexually explicit photographs. He also gets really turned on when his lover undresses in front of him. Joe's behavior might be described as
A) fetishistic.
B) frotteuristic.
C) voyeuristic.
D) normal.
# 1.21
(1 pts.) John gets nauseous when he thinks about having sexual intercourse and he actively avoids the sexual advances of others. John might be diagnosed as having
A) male erectile disorder.
B) sexual aversion disorder.
C) dyspareunia.
D) inhibited male orgasm disorder.
# 1.27
(1 pts.) Five-year-old Timmy has older sisters who dress him up occasionally and call him "Timbelina" since they really wanted a little sister instead of a little brother. If this pattern continues it is possible that Tim might develop
A) sexual masochism.
B) sexual sadism.
C) pedophilia.
D) transvestic fetishism.
# 1.29
(1 pts.) Carol is extremely interested in sex but does not experience the vaginal changes that ordinarily precede sexual intercourse. Carol may have
A) sexual aversion disorder.
B) hypoactive sexual desire disorder.
C) inhibited female orgasm disorder.
D) female sexual arousal disorder.
# 1.32
(1 pts.) John is in a p.
I Headnotes and indexes are copyrighted and may not be duplica.docxeugeniadean34240
I Headnotes and indexes are copyrighted and may not be duplicated by photocopying, printing.
I or other means without the express permission of the publishers. 1 -800-351-0917
43 Fla. L. Weekly S512 SUPREME COURT OF FLORIDA
Committee later submitted a revised proposal in response to comments. While we
generally approve the Committee's revisions, the revised proposal would have allowed
twenty days[ ratherthan ten, to serve a reply brief. In order to maintain consistency with
otherprovisions in rule 9.146(g)(3)(B), we haverevised the Committee's proposal such
that parties are allowed twenty days to respond after the last initial brief, and ten days
to respond after the last answer brief.
3Wehave revised the Committee's proposal to refer specifically to requirements for
electronic service in Rule ofJudicial Administration 2.516(b).
"See CoastalDev. ofN. Fla.,Inc. v. City ofJacksonville Beach, 788 So. 2d 204,205
footnotes.
(a) Florida Supreme Court.
(111887-present: Fenelonv. State. 594 So. 2d 292 (Fla. 1992).
{211846-1886: Livingston v. L 'Engle, 22 Fla. 427 (1886).
J ±' C-fl&LL/fl 1
n.3(Fla.20CII); Fla. Power &Light Co. v.CityofDania,76l So.2d 1089,1094 (Fla.
2000) ("No statewide criterion exists at this time."); see also Broward Cty. v. G.B. V.
Intern., Ltd.
Anstead,J.)
, 787 So. 2d 838, 849-53 (Fla. 2001) (Pariente, J., dissenting, joined by
(LEWIS, J., concurring in part and dissenting in part.) I dissent
because there is no need to amend the rule with regard to joinder on
appeal. This amendment is likely to generate more confusion than
clarity. I concur with the remainder ofthe amendments.
! * * *
I ■
! ..■■■■
Rules of Appellate Procedure—Amendment—Uniform Citation
System
IN RE: AMENDMENTS TO FLORIDA RULE OF APPELLATE PROCEDURE
9.800. Supreme Court of Florida. Case No. SC17-999. October 25,2018. Original
Proceeding—Florida Rules of Appellate Procedure. Counsel: Courtney Rebecca
Brewer, Ch lir, Appellate CourtRules Committee, Tallahassee, Kristin A. Norse, Past
Chair, App sllate Court Rules Committee, Tampa; and Joshua E. Doyle, Executive
Director, and Heather Savage Telfer, Staff Liaison, The Florida Bar, Tallahassee, for
Petitioner.
(PER CUjRIAM.) This matter is before the Court for consideration of
proposed, amendments to Florida Rule ofAppellate Procedure 9.800
(Uniforn
Fla. Cons t.
TheFlorida Bar's Appellate CourtRules Committee (Committee)
proposes
uniform
proposal
Citation System). We havejurisdiction. See art. V, § 2(a),
amendments to rule 9.800 to substantially update the
citation formats provided in that rule. The Committee's
to amend the rule was first presented to the Court in the
Commirt 5e' s regular-cycle report ofproposed rule amendments in In
re Amendments to the Florida Rules ofAppellate Procedure—2017
Regular-Cycle Report, No. SC17-152 (Fla. report filed Jan. 31,
2017).' The Court, on its own motion, entered an order directing that
the proposed amendments to rule 9.800 be .
Students, digital devices and success - Andreas Schleicher - 27 May 2024..pptxEduSkills OECD
Andreas Schleicher presents at the OECD webinar ‘Digital devices in schools: detrimental distraction or secret to success?’ on 27 May 2024. The presentation was based on findings from PISA 2022 results and the webinar helped launch the PISA in Focus ‘Managing screen time: How to protect and equip students against distraction’ https://www.oecd-ilibrary.org/education/managing-screen-time_7c225af4-en and the OECD Education Policy Perspective ‘Students, digital devices and success’ can be found here - https://oe.cd/il/5yV
We all have good and bad thoughts from time to time and situation to situation. We are bombarded daily with spiraling thoughts(both negative and positive) creating all-consuming feel , making us difficult to manage with associated suffering. Good thoughts are like our Mob Signal (Positive thought) amidst noise(negative thought) in the atmosphere. Negative thoughts like noise outweigh positive thoughts. These thoughts often create unwanted confusion, trouble, stress and frustration in our mind as well as chaos in our physical world. Negative thoughts are also known as “distorted thinking”.
Instructions for Submissions thorugh G- Classroom.pptxJheel Barad
This presentation provides a briefing on how to upload submissions and documents in Google Classroom. It was prepared as part of an orientation for new Sainik School in-service teacher trainees. As a training officer, my goal is to ensure that you are comfortable and proficient with this essential tool for managing assignments and fostering student engagement.
Unit 8 - Information and Communication Technology (Paper I).pdfThiyagu K
This slides describes the basic concepts of ICT, basics of Email, Emerging Technology and Digital Initiatives in Education. This presentations aligns with the UGC Paper I syllabus.
How to Make a Field invisible in Odoo 17Celine George
It is possible to hide or invisible some fields in odoo. Commonly using “invisible” attribute in the field definition to invisible the fields. This slide will show how to make a field invisible in odoo 17.
This is a presentation by Dada Robert in a Your Skill Boost masterclass organised by the Excellence Foundation for South Sudan (EFSS) on Saturday, the 25th and Sunday, the 26th of May 2024.
He discussed the concept of quality improvement, emphasizing its applicability to various aspects of life, including personal, project, and program improvements. He defined quality as doing the right thing at the right time in the right way to achieve the best possible results and discussed the concept of the "gap" between what we know and what we do, and how this gap represents the areas we need to improve. He explained the scientific approach to quality improvement, which involves systematic performance analysis, testing and learning, and implementing change ideas. He also highlighted the importance of client focus and a team approach to quality improvement.
The Indian economy is classified into different sectors to simplify the analysis and understanding of economic activities. For Class 10, it's essential to grasp the sectors of the Indian economy, understand their characteristics, and recognize their importance. This guide will provide detailed notes on the Sectors of the Indian Economy Class 10, using specific long-tail keywords to enhance comprehension.
For more information, visit-www.vavaclasses.com
The French Revolution, which began in 1789, was a period of radical social and political upheaval in France. It marked the decline of absolute monarchies, the rise of secular and democratic republics, and the eventual rise of Napoleon Bonaparte. This revolutionary period is crucial in understanding the transition from feudalism to modernity in Europe.
For more information, visit-www.vavaclasses.com
The Roman Empire A Historical Colossus.pdfkaushalkr1407
The Roman Empire, a vast and enduring power, stands as one of history's most remarkable civilizations, leaving an indelible imprint on the world. It emerged from the Roman Republic, transitioning into an imperial powerhouse under the leadership of Augustus Caesar in 27 BCE. This transformation marked the beginning of an era defined by unprecedented territorial expansion, architectural marvels, and profound cultural influence.
The empire's roots lie in the city of Rome, founded, according to legend, by Romulus in 753 BCE. Over centuries, Rome evolved from a small settlement to a formidable republic, characterized by a complex political system with elected officials and checks on power. However, internal strife, class conflicts, and military ambitions paved the way for the end of the Republic. Julius Caesar’s dictatorship and subsequent assassination in 44 BCE created a power vacuum, leading to a civil war. Octavian, later Augustus, emerged victorious, heralding the Roman Empire’s birth.
Under Augustus, the empire experienced the Pax Romana, a 200-year period of relative peace and stability. Augustus reformed the military, established efficient administrative systems, and initiated grand construction projects. The empire's borders expanded, encompassing territories from Britain to Egypt and from Spain to the Euphrates. Roman legions, renowned for their discipline and engineering prowess, secured and maintained these vast territories, building roads, fortifications, and cities that facilitated control and integration.
The Roman Empire’s society was hierarchical, with a rigid class system. At the top were the patricians, wealthy elites who held significant political power. Below them were the plebeians, free citizens with limited political influence, and the vast numbers of slaves who formed the backbone of the economy. The family unit was central, governed by the paterfamilias, the male head who held absolute authority.
Culturally, the Romans were eclectic, absorbing and adapting elements from the civilizations they encountered, particularly the Greeks. Roman art, literature, and philosophy reflected this synthesis, creating a rich cultural tapestry. Latin, the Roman language, became the lingua franca of the Western world, influencing numerous modern languages.
Roman architecture and engineering achievements were monumental. They perfected the arch, vault, and dome, constructing enduring structures like the Colosseum, Pantheon, and aqueducts. These engineering marvels not only showcased Roman ingenuity but also served practical purposes, from public entertainment to water supply.
250 words, no more than 500· Focus on what you learned that made.docx
1. 250 words, no more than 500
· Focus on what you learned that made an impression, what may
have surprised you, and what you found particularly beneficial
and why. Specifically:
· What did you find that was really useful, or that challenged
your thinking?
· What are you still mulling over?
· Was there anything that you may take back to your classroom?
· Is there anything you would like to have clarified?
Your Weekly Reflection will be graded on the following criteria
for a total of 5 points:
· Reflection is written in a clear and concise manner, making
meaningful connections to the investigations & objectives of the
week.
· Reflection demonstrates the ability to push beyond the scope
of the course, connecting to prior learning or experiences,
questioning personal preconceptions or assumptions, and/or
defining new modes of thinking.
BELOW ARE LESSON COVERED
· This week's investigations introduce and explore one of the
most common distributions (one you may be familiar with): the
Normal Distribution. In our explorations of the distribution and
its associated curve, we will revisit the question of "What is
typical?" and look at the likelihood (probability) that certain
observations would occur in a given population with a variable
that is normally distributed. We will apply our work with
Normal Distributions to briefly explore some big concepts of
inferential statistics, including the Central Limit Theorem and
Hypothesis Testing. There are a lot of new ideas in this week’s
work. This week is more exploratory in nature.
Goals:
· Explore the Empirical Rule
· Become familiar with the normal curve as a mathematical
model, its applications and limitations
2. · Calculate z-scores & explain what they mean
· Use technology to calculate normal probabilities
· Determine the statistical significance of an observed
difference in two means
· Use technology to perform a hypothesis test comparing means
(z-test) and interpret its meaning
· Use technology to perform a hypothesis test comparing means
(t-test) (optional)
· Gather data for Comparative Study Final Project.
·
DoW #5: The SAT & The ACT
Two Common Tests for college admission are the SAT
(Scholastic Aptitude Test) and the ACT (American College
Test). The scores for these tests are scaled so that they follow a
normal distribution.
· The SAT reported that its scores were normally distributed
with a mean μ=896 and a standard deviation σ=174
· The ACT reported that its scores were normally distributed
with a mean μ=20.6 and a standard deviation σ=5.2.
We have two questions to consider for this week’s DoW:
2. A high school student Bobby takes both of these tests. On the
SAT, he achieves a score of 1080. On the ACT, he achieves a
score of 30. He cannot decide which score is the better one to
send with his college applications.
. Question: Which test score is the stronger score to send to his
colleges?
· A hypothetical group called SAT Prep claims that students
who take their SAT Preparatory course score higher on the SAT
than the general population. To support their claim, they site a
study in which a random sample of 50 SAT Prep students had a
mean SAT score of 1000. They claim that since this mean is
higher than the known mean of 896 for all SAT scores, their
program must improve SAT scores.
. Question: Is this difference in the mean scores statistically
significant? Does SAT Prep truly improve SAT Scores?
.
3. Investigation 1: What is Normal?
One reason for gathering data is to see which observations are
most likely. For instance, when we looked at the raisin data in
DoW #3, we were looking to see what the most likely number of
raisins was for each brand of raisins. We cannot ever be certain
of the exact number of raisins in a box (because it varies) no
matter how much data we gather. But, we can estimate a likely
value or range for the number of raisins and determine the
empirical probability that a box of raisins would be in this
range.
In Activities A & B, we explore the probabilities seen in a
particularly symmetric distribution.
.
Inv 1, Activity A: Probability in a Distribution
Excerise A1: Relative Frequency
Histograms
Relative frequency histograms provide information about
probabilities. Consider the following relative frequency
histogram for the number of raisins in a 1/2 ounce box of Brand
B raisins
(The probability for each interval in the histogram is displayed
at the top of the bar for that interval.)
(a) Describe the shape of the distribution.
(b) Suppose I pick a random box of Brand B raisins. Based on
this data, what is the probability that the number of raisins in
the box is:
· greater than 28?
· less than or equal to 28?
· exactly 28?
· greater than 32?
· between 26 and 30 (inclusive)?
Answers: i) 32%; ii) 69%; iii) 23%; iv) 0%; v) 71%
4. A common way to "divide up" the histogram is to use the
standard deviation as a ruler. We will consider the data in
groups that are one, two and three standard deviations from the
mean. Let's start by looking at the group of data that is within
one standard deviation of the mean:
One Standard Deviation from the Mean:
We can add these values to our graph to see the group within
one standard deviation of the mean:
Exercise A2:Use the above histogram to:
(a) determine the probability that a random box of brand B
raisins would fall between 25.8 and 29.4 (within one standard
deviation of the mean)
(b) calculate the values that are two standard deviations away
from the mean. Sketch them on the graph.
(c) determine the probability that a random raisin box would
fall within two standard deviations of the mean.
(d) Repeat steps b and c for raisin boxes that fall within three
standard deviations from the mean.
(e) Summarize your work from this exercise in a table like the
one shown below:
Percentage of Observations
Brand B Raisins
Within 1 standard deviation of the mean
Within 2 standard deviations of the mean
within 3 standard deviations of the mean
5. Exercise A3: The following distribution shows a relative
frequency histogram of students scores on a Math placement
exam. Like the Brand B Raisins distribution, it is a roughly
symmetric, mound-shaped distribution.
(a) Determine the probability that a random student's score
would fall within one standard deviation of the mean; within
two standard deviations of the mean; and within three standard
deviations of the mean.
(b) Add your findings to the table you started in Exercise A2,
by adding a column for Math Placement Exam Scores:
Percentage of Observations...
Brand B Raisins
Math Placement Exams Scores
within 1 standard deviation of the mean
within 2 standard deviations of the mean
within 3 standard deviations of the mean
Our findings illustrate a “big idea” called the Empirical Rule:
THE EMPIRICAL RULE
(68-95-99.7%)
6. In "special" symmetric, mound-shaped distributions, about 68%
of the observations fall within one standard deviation, about
95% fall within two standard deviations, and about 99.7%
(nearly all) all within three standard deviations.
Exercise A5: Practice with the Empirical Rule
Each of the distributions shown below is a symmetric, mound-
shaped distribution with a mean of 0 and a standard deviation of
1. Use the empirical rule to determine the percentage of
observations represented by the shaded area on each
distribution.
(answers follow)
1. Between -2 and 2
2. More Than 2 or Less Than -2
3. Greater Than -1
4. Greater than 1
Answers: (1) 95%, (2) 5%, (3) 84%, (4) 16%
·
Inv 1, Activity B: The Normal Distribution
The "special" symmetric, mound-shaped distributions that
follow the Empirical Rule (like the ones you looked at in
investigation 1 are called Normal Distributions. Normal
distributions are a family of distributions with very specific
properties, though the way most of us think of them is as a "bell
curve." The key properties we think of for a normal distribution
are:
· One peak in the middle (mean)
· Symmetric about the mean
· Follows the Empirical Rule: 68-95-99.7
These are not the only defining characteristics of a normal
distribution. Normal distributions are defined by equations,
7. which dictate specifics about the shape of the mound, how it
curves, and the areas beneath the different sections. However,
for most situations you will encounter, mound-shaped
symmetric distributions can be considered to be nearly normally
distributed.
Why are they called normal? For starters, many variables in
many different contexts follow the normal distribution, making
this distribution the typical, expected or "normal" pattern. When
we talk about skewed distributions, we usually mean "skewed
from the normal."
The samples you worked with in Investigation 1 (the raisin
boxes or the math placement scores) are displayed with
histograms. The histograms are roughly symmetrical and
mound-shaped. They approximate the theoretical normal curve
that represents the entire population. The graph below shows
the theoretical normal curve superimposed on the distribution of
the Brand B raisin data:
Notice that this sample of 22 raisin boxes nearly fills the area
beneath the theoretical curve. The normal curve models what we
think the true population distribution should be.
The histogram shows the distribution of the actual sample data.
As such, its mean and standard deviation are statistics,
represented by μ and s, respectively.
· The normal curve shows the distribution of the theoretical
population, so its mean and standard deviation are parameters,
represented by μ and σ.
Complete the following activities about Normal Distributions:
Exercise B1 Watch the video clip entitled, "4. Normal
Distributions" in the Annenberg Series Against All Odds.
8. As you watch, take notes on the following questions:
· What is a density curve? How is it related to a histogram or
other display of a distribution?
· What properties does a Normal Curve have?
· What are some variables that are normally distributed? What
is it about them that makes them normally distributed?
· Why are the Normal Curves considered to be a family?
· What is the formula for standardizing an observation? Why
would you want to standardize?
·
Inv 1, Activity C: Applying the Empirical Rule
Normal distributions are entirely defined by the mean and
standard deviation of the distribution. When we know these two
values, we have the full picture of the distribution of a variable
for the population. From this, we can sketch the distribution and
determine the likelihood of specific events occurring (using the
empirical rule and other methods.) This is the purpose of the
following example:
Examples:The Scenario
At Lesley Middle School, all students were timed when they ran
a 100m dash. It was found that the data was normally
distributed with a mean of 17.2 seconds and a standard
deviation of 2.1 seconds.
· What range of times would you expect to be typical for the
100m dash at this school? (let’s say that “typical” would mean
at least 95% of students would be in this range)
· A student ran the 100 m dash in 10.9 seconds. How likely is it
that a student could run the 100 m dash in 10.9 seconds or less?
First, Picture it
In this scenario, we know everything we need to know to get a
picture of this data. So, let's make the graph. We know it is
normally distributed - this gives us the general shape The graph
need not be perfectly to scale, but it should show the inflection
points – places where the curvature switches. Recall from the
Annenberg video that inflection points are found 1 standard
deviation from the mean.
9. Next, label the mean and the values of the points that are 1
standard deviation above and below the mean of the graph.
Lastly, label the points that are 2 and 3 standard deviations
from the mean.
Then, Apply the Empirical Rule to answer the questions:
1. The Empirical Rule states that 95% of the data will lie within
2 standard deviations of the mean. For this scenario, that would
be roughly between 13 second and 21.4 seconds.
So we can say that a typical range of times for middle schoolers
at Lesley Middle School is between 13 and 21.4 seconds,
because 95% of all students would have times in this range.
2. Times that are as fast or faster than 10.9 seconds would be
more than 3 standard deviations from the mean.
From the Empirical rule, we know that 99.7% of the data is
within 3 standard deviations of the mean. This means that 0.3%
is within the two tails. So the likelihood of having a time that is
10.9 second or less would be HALF of 0.3%, or 0.15%. This is
very unlikely – Perhaps this student is a truly exceptional
athlete; or perhaps there was an error in recording this time? A
probability this low warrants extra attention.
Exercise C1: SAT scores from DoW #5: In DoW #5, we are
given thatthe SAT (Scholastic Aptitude Test) scores are
normally distributed with μ=896 and σ=174.
10. (a) Sketch a normal curve for this distribution, with three
standard deviations from the mean marked out.
(b) What range of scores is "typical" for this test (with “typical”
meaning 95% students score in this range)?
(c) What is the probability that a student would score above
1418?
(d) What is the approximate probability that a student would
score between 1200 and 1400? Explain how you found this
answer.
Exercise C2: ACT scores from DoW #5: In DoW #5, we are
given that ACT (American College Test) scores are normally
distributed with μ=20.6 and σ=5.2.
(a) Sketch a normal curve for this distribution, with three
standard deviations from the mean marked out.
(b) What range of scores is "typical" for this test? (with
“typical” meaning 95% of students score in this range)
(c) What is the probability that a student would score below
15.4?
(d) What is the approximate probability that a student would
score between 15 and 30? Explain how you found this answer.
Exercise C3: Bobby’s Test Scores: In DoW #5, we learn that
Bobby scored 1080 on the SAT and 30 on the ACT. Consider
your work in Exercises C1 and C2. Which score do you think
Bobby should send to his colleges? Why?
Post your response to Exercise C3 to the Discussion Thread “
DoW#5: Bobby's Scores” by Tuesday, 10 PM EST. Review the
posts of others and make at least two follow-up posts by
Thursday, 10 PM ESTDo Not Read On until you have completed
these exercises: the answer to Exercise C3 is discussed in
Activity D.
·
Inv 1, Activity D: Beyond the Empirical Rule
In Exercise C3, Bobby’s scores were not an even number of
standard deviations away from the mean. This makes comparing
11. them (and determining the probabilities associated with those
scores) difficult (though not impossible). There are ways of
determining the probabilities when the desired values are not 1,
2, or 3 standard deviations from the mean. We will explore one
such approach in this investigation.
Recall that all normal curves are members of the same family.
By changing the mean, you can alter the location of the curve
(shift it left or right). By changing the standard deviation, you
can alter the height and width of the curve. These properties
allow us to compare values from different curves by
standardizing the data.
Consider the graphs below, showing the normal curves for the
SAT and ACT from the last investigation. Added beneath each
is a new scale, showing the number of standard deviations from
the mean.
This rescaling allows us to compare values for each of the
distributions by looking at how many standard deviations the
values are from the mean. Now, we need to calculate how many
standard deviations Kathy's score and Bobby's score are from
the mean of its distribution. We do this using the
standardization formula:
Where x is a specific observation, μ is the population mean and
σ is the population standard deviation.
This shows that Bobby’s ACT score is a greater number of
deviations from the mean. On a standardized normal curve
(where μ=0 and σ=1), we can compare the two scores:
Two ways you can think of this are:
12. · The percentage of students scoring Bobby’s score (or higher)
on the ACT is less than the percentage of students scoring
Bobby's score (or higher) on the SAT.
· Bobby’s ACT score is higher than Bobby's SAT score, relative
to their respective means.
So, the ACT score is the stronger college test score!
Z-scores are useful for comparing data; in addition, they are
useful for finding probabilities that we cannot find with the
Empirical Rule alone. Suppose we wanted to know the
probability that a student would score as high as Bobby, or
higher:
From the Empirical Rule, we know that 47.5% of students
would score between 20.6 and 31.0 (2 standard deviations). So,
we could estimate the percentage above Bobby’s ACT score of
30 to be a little more than 2.5% (50% - 47.5%).
We can determine a more exact percentage using the graphing
calculator. The graphing calculator can calculate the probability
that a z-score is between two values on a standard normal curve
using the function normalcdf:
Press [2nd][VARS] and select Normalcdf(
To determine the probability that a student scored higher than
Bobby on the ACT (above 1.81 standard deviaions) we are
looking at the part of the graph between 1.81 and positive
infinity. So, enter:
normalcdf(1.81, 99999) = 3.5%
Notice that the second value, 99999, is an arbitrary large
postive number. Since the area under the curve becomes so
small as the z-scores get larger and larger, this value will give
an accurate percentage. We have used the calculator to
determine that the probability that a student would score as high
as Bobby on the ACT is 3.5%. In other words, P(z>1.81)=3.5%
An alternate option to the graphing calculator is this online
13. convertor.
Since we are only interested in greater than choose one tailed.
Insert 1.81 for the z score. Click submit and you will get the
same answer.
Exercise D1. Use the graphing calculator to determine the
probability that a student would score as high as Bobby on the
SAT.
Exercise D2: Use the graphing calculator to determine the
following normal distribution probabilities:
(a) P(z<1.28)
(b) P(z>1.28)
(c) P(z< -2.25)
(d) P(-1.1<z<1.1)
Answers: D1) 14.5
Answers: D2. a) 90.0% ;b) 10.0%; c) 1.2%; d) 72.9%
The calculator function normalcdf( ) will also calculate
probabilities without the use of a z-score. Let's revisit Bobby’s
ACT score one more time. He scored a 30 on the ACT, which
has m=20.6 and s=5.2. We can use the graphing calculator to
find the probability that a student would score 30 or higher on
the ACT without first finding a z-score. To do this, enter:
normalcdf( minimum, maximum,m, s)
normalcdf( 30, 99999, 20.6, 5.2)
This gives the same percentage we found earlier using Bobby’s
ACT z-score (3.5%).
Another option for this is to use this link.
You will insert 20.6 for the mean, 5.2 for standard deviation,
and 30 for x. This will give you a cumulative probabilty of
.96467. The percent above this is nearly the same answer of
3.5%
Exercise D3: Use the graphing calculator to recalculate Bobby’s
14. SAT probability, as we just did for his ACT probability.
·
Investigation 2: Testing Hypotheses
The second part of DoW #5 asks us to evaluate a claim based on
sample data: is the sample of scores from SAT Prep students
different from other SAT scores, in a way that is more than just
random variation. This question is asking us to take what we
know about SAT scores – they follow a normal distribution,
with a mean of 896 and a standard deviation of 174 – and infer
whether or not a sample mean SAT score of 1000 is “not
normal”. Certainly, students score higher than 1000 all the
time…but the question is,
“How likely is it that a whole group of 50 students would have
an average score that is a full 100 points above the mean of
896? Couldn’t this just be due to normal variation?”
This investigation looks at how to address this question
statistically.
·
Inv 2, Activity E: Sample Means are Normal
Exercise E1: Consider the question posed above: “How likely is
it that a whole group of 50 students would have an average
score that is a full 100 points above the mean of 896? Couldn’t
this just be due to normal variation?”
What are your initial thoughts on this question? Do you think
SAT Prep’s results support their claim that they raise SAT
scores? Record your initial thoughts in your journal.
In the SAT Prep claim, they refer to the mean of a sample of 50
scores. It is hard to compare a mean of 50 scores to the mean
for the whole population. To better understand this situation, we
need to look at LOTS of samples of 50 scores from the whole
population, and get an idea of what their means look like.
Exercise E2: Complete the Central Limit Theorem document.
15. In this exercise, you will run a virtual experiment to collect
random samples of 50 SAT scores and calculate their means.
This will produce a distribution of sample means, that you can
compare to the sample mean for SAT Prep.
Exercise E3: In Exercise E2, you answered the question, “do
you think there sufficient evidence to conclude that SAT Prep
improves SAT scores, as they claim?”
Post your response to this question to your group’s DB for DoW
#5:SAT Prep by Friday, 11:59 PM EST.
Review the responses of your group. Consider your work in the
remainder of this investigation. Post at least three meaningful
responses to your group by Sunday, 11:59 PM EST.
In these exercises, you created a portion of a Sampling
Distribution for the Means: a distribution of the means from lots
of different samples. The true sampling distribution for the
means would have EVERY mean from EVERY possible random
sample of 50 test scores. The distribution in Part II, with 355
scores, is very close to the true sampling distribution for the
means:
You probably noticed that this distribution has nearly the same
mean as the SAT scores population mean score (896). However,
its spread is MUCH MUCH smaller. In fact, the standard
deviation of the sampling distribution is a fraction of the
original standard deviation (174). This should make sense – in
the population, individual students will have scores that are
very high and very low. But, within a sample of 50 students,
those highs and lows will “average out” bringing the overall
mean of the sample closer to the true population mean.
This observation reflects a major theorem in statistics – the
Central Limit Theorem.
16. The Central Limit Theorem states that if you have sample sizes
larger than 30, the sample means will be nearly normal
distributions.
· The mean of the sampling distribution will be the same as the
population mean.
· The standard deviation of the sampling distribution will be
population standard deviation divided by the square root of the
sample size.
Note: One powerful part of the Central Limit Theorem is that
the population does NOT have to be normally distributed itself
to have a sampling distribution that is normally distributed
For our example, the SAT Prep sample is larger than 30 (it is
50). By the Central Limit Theorem, all samples of size 50 will
have means that follow a normal distribution. This normal
distribution will have a mean of 896 (the same as the mean for
the population of SAT scores). BUT, the standard deviation will
be much much smaller: 174/sqrt(50) = 24.6. This tells us that
the mean scores for groups of 50 students will not vary much -
they will be very close to the center of the distribution.
Population of SAT Scores
m = 896 s = 174
Sampling Distribution of Means
from samples of
50 Scores
s = 24.6
With the SAT Prep sample, we can now calculate the
probability of a random sample of 50 SAT scores having a mean
of 1000:
Normalcdf( 1000, 99999999, 896, 24.6) = 0.00001
This is an incredibly low probability – it is highly unlikely that
17. the sample of SAT Prep students is “the same” as other samples
of 50 students.
·
Inv 2, Activity F: Hypothesis Testing
The process of using statistics to test the validity of claim is
part of a branch of statistics called Inferential Statistics. Up to
this point, our course has focused primarily on Descriptive
Statistics.
Descriptive Statistics are used to summarize and describe the
data. Tools like histograms, box plots, mean, median, and
standard deviation all describe and summarize. Descriptive
statistics allow us to describe the distribution and make
comparisons among distributions.
Inferential Statistics is a use of statistics to make an inference
beyond what is immediately known from the data. Sometimes
this involves estimating the true value of a population parameter
(like estimating the true mean number of raisins in a ½ oz box
of raisins). It also involves using statistics to support or
disprove a hypothesis, as we did with the claim by SAT Prep.
The process of evaluating a hypothesis is called Hypothesis
Testing. In Activity E, you looked at an overview of the
process: we started with a claim, we found a way to calculate
the likelihood of the claim, and we used this to determine
whether or not the claim was probable. The actual process of
Hypothesis Testing is more technical. We will touch the surface
of this concept in the next two activities.
Exercise F1: Watch the video 25.Tests of Significnace in the
Annenberg Series, Against All Odds.
As you watch, take notes on:
· The Steps of hypothesis Testing
· What is a p-value?
· What is meant by statistically significant?
· What is the difference between a one-tail test and a two-tail
test.
18. · Optional Informationon Tailed tests
The Steps of a Hypothesis Test:
· State a Null Hypothesis: H0
This is generally a statement that is assumed to be true or based
on a known truth.
· State the Alternative Hypothesis: HA
This is the statement you are trying to support
· Determine the desired level of significance a (alpha)
This is the probability level that would allow you to reject the
Null Hypothesis with Confidence.
· Calculate the p-value
This is the probability of your observed results
· Compare the p-value to the level of significance a
If the p-value is below the level of significance, then the H0 is
rejected in favor of the HA; if not, H0 remains the operating
hypothesis. It is important to note the H0 is never PROVEN. It
can be supported by the data or discredited by the data.
Likewise, HA is never PROVEN. It can become the new
hypothesis, because the old hypothesis is discredited. This is
not proof of certainty.
Example: Perform a hypothesis test for our work with SAT Prep
in DoW #5
· H0: The sample mean score of the SAT Prep students is the
same as the population mean score for all SAT students.
H0:
· HA: The sample mean score of the SAT Prep students is
greater than the population mean score for all SAT Students
HA: Note: We had three choices for the HA. The sample mean
() could be greater than the population mean, less than the
population mean, or just not equal to the population mean. We
chose greater than here, because the claim is that SAT Prep
improves the scores.
· The level of significance can vary from situation to situation.
A strong level of significance is ( 0.5%).
19. In this setting, we mean that IF the probability of the sample of
50 SAT Prep students having a mean score of 1000 is LESS
THAN 0.5% under H0, we would consider it to be statistically
significant and that H0 would be rejected.
· Calculate the p-value for the sample mean.
We did this when we talked about Central Limit Theorem
earlier. Recall the sampling distribution:
s = 24.6
Based on this, we calculate the probability of getting a sample
mean at or above 1000:
p =Normalcdf( 1000, 99999999, 896, 24.6) = 0.00001
This means that if the sample of 50 SAT Prep scores truly were
the same as every other sample of 50 scores, the likelihood of
getting a sample mean as high as 1000 would be 0.00001or
.01% – highly unlikely!
· Since the p-value (.0001) is well below the level of significant
(0.5%), we reject the null hypothesis in favor of the alternative
hypothesis. We now assume that the mean score of the SAT
Prep students is higher than the mean SAT score for the
population.
·
Inv 2, Activity H: Hypothesis Testing
Evaluating a hypothesis test can be done using the graphing
calculator or online tools. There are two hypothesis tests to be
familiar with for testing sample means. This Activity introduces
you to these two tests.
Exercise H1: Complete a hypothesis test comparing the Sample
Mean for SAT Prep to the known population mean for the SAT
using Hypothesis Test Mean. This video describes how to do the
T-test on a TI-84 or 83.
20. This link provides a calculator for the Hypothesis Test Mean.
http://easycalculation.com/statistics/hypothesis-test-population-
mean.php
Exercise H2: Complete a hypothesis test comparing two sample
mean SAT Scores using Hypothesis Test 2 Means. This video
describes how to do the T-test for two means on the TI-84 or
83.
Diversity in the
Key Assignment
Mathematics Classroom
EQUITY IN MATHEMATICS EDUCATION
Research Assignment
Select a subgroup from the NCTM’s recommended subgroups
list located near the bottom of this page. It is suggested that
you choose a group with which you have little or no
professional experience. Acquaint yourself with some of the
literature that supports work with learners who identify with
your chosen group. Supporting articles may be found at
http://www.nctm.org/search.aspx?c=all&q=Equity by entering
the name of your desired subgroup in the Search Box.
1. create a list of 10 (or more if you are so inclined) important
21. considerations that would aide in guiding teachers in their work
with diversified math learners within their classrooms
2. This list should be carefully crafted, articulate and
comprehensive
◦The list should reflect the overarching themes of the articles
(i.e., what did you highlight, what are the salient themes?)
3. Provide a short (paragraph) reflection on the importance of
such an activity and the relevance this has in your role as an
educator
•Your Key assignment should include:
◦A brief introduction about the topic you chose and why (just a
few sentences)
◦A bulleted list (of your 10 or so items) (This can also be in
table form, etc)
◦A closing paragraph that serves as a reflection (importance of
such an activity and the relevance this has in your role as an
educator)
◦List of references
The NCTM Subgroups are:
· AT-RISK LEARNERS
· ENGLISH LANGUAGE LEARNERS
· GENDER EQUITY
· GIFTED STUDENTS
· MINORITY STUDENTS
· SPECIAL NEEDS/DISABILITIES
22. Please refer to the Equity in Mathematics Education: Research
Assignment rubric for additional details about the scoring
criteria.
Rubric for Key Assessment Equity in Mathematics Education-
Research Assignment
Course:
(Diversity in the Mathematics Classroom)
Standard / Competency addressed
Criteria
4
Distinguished
3
Proficient
2
Developing Skills
1
Unsatisfactory
Common Core State Standards
Standards for Mathematical Practice #5: Use Appropriate Tools
Strategically.
A mathematically proficient student at various grade levels is
able to identify relevant external mathematical resources, such
as digital content located on a website, and use them to pose or
solve problems. The student is able to use technological tools to
explore and deepen his/her understanding of concepts.
Student supplies additional addresses of at least 4 websites
chosen to augment information gathered on the NCTM website.
A clear and concise explanation of why these websites were
23. chosen, is provided.
Student supplies additional addresses of 2 websites chosen to
augment information gathered on the NCTM website. A suitable
explanation of why these websites were chosen, is provided.
Student supplies additional address of 1 website chosen to
augment information gathered on the NCTM website. Explains
why this websites was chosen, but offers limited detail.
Student supplies no additional addresses of any website that
would augment information gathered on the NCTM website, or
offers no explanation as to why any website was selected.
Common Core State Standards
ELA
College and Career Readiness Anchor Standards for Writing #7
Produces clear and coherent writing in which the student
extracts an overall thesis from the research.
Student clearly, with clear and coherent writing, extracts an
overall thesis from the literature.
Student adequately extracts an overall thesis from the literature,
and presents it in an organized fashion.
Student presents an underdeveloped review of the academic
literature while making an inadequate attempt to extract an
overall thesis.
Student presents a deficient review of academic literature, and
makes no attempt to extract an overall thesis.
Common Core State Standards
ELA
College and Career Readiness Anchor Standards for Writing #7
Summarizes the research while producing clear and coherent
writing.
Student clearly, coherently and adeptly paraphrases or
summarizes the research, while developing major ideas in
his/her own scholarly voice.
24. Student summarizes the research, developing major ideas with
good clarity.
Student is sometimes unclear as s/he summarizes the research
ideas from the literature.
In a manner that is unclear and incoherent, the student
summarizes the research from the literature.
Common Core State Standards
ELA
College and Career Readiness Anchor Standards for Writing #7
Produce clear and coherent writing in which the thematic
connections between sources are drawn.
Student shows that thematic connections between sources are
clearly drawn and coherently explained.
Student identifies some of the thematic connections between
sources, and provides a thoughtful explanation of these
connections.
Student identifies some of the thematic connections between
sources, but provides an explanation that demonstrates little
thought towards understanding of these connections.
Student presents a poor understanding of thematic connections
between sources.
Common Core State Standards
ELA
College and Career Readiness Anchor Standards for Writing #7
Produce clear and coherent writing in which organization, is
appropriate to task, purpose, and audience, by providing a list
of 10 considerations from the Equity subgroup.
Student provides a list of 10 considerations from the Equity
subgroup and demonstrates that each of the 10 considerations is
clearly distinguishable from the others.
Student develops a list of 10 considerations from the Equity
subgroup that was selected, but some of these exhibit
25. unnecessarily overlapping ideas.
Student develops a list of fewer than, or more than, 10
considerations from the Equity subgroup that was selected, or
exhibits a problem in clarity of expression.
Student develops a list of fewer than, or more than, 10
considerations from the Equity subgroup that was selected, that
are irrelevant or unsatisfactory overall.
Common Core State Standards
ELA
College and Career Readiness Anchor Standards for Writing #7
Produce clear and coherent writing in which the development,
organization, and style are appropriate to task, purpose, and
audience, reflecting high academic standards.
Student carefully balances his/her own ideas with those of
others, while respectfully challenging “group-mates” to
maintain high academic standards.
Student integrates his/her own ideas with those of others, while
encouraging maintenance of high academic standards.
Student offers few ideas in the process of group assignment.
Relies on “group-mates” to do much of the work. High
academic standards are being compromised.
Student participation in group work is limited or unsatisfactory.
There is no evidence of high academic standards.
Common Core State Standards
ELA
College and Career Readiness Anchor Standards for Writing #7
The student produces thoughtful feedback to peers’ suggested
revisions.
26. Student shows that evaluation of peers’ suggested revisions is
apparent. Through thoughtful integration of feedback, shows
expanded ideas.
Student incorporates peers’ suggested revisions without
compromising the thread of the initial ideas.
Student takes peers’ suggested revisions lightly, with little
thoughtful reflection.
Student demonstrates no evidence of feedback or contributing
toward peers’ suggested revisions.
Common Core State Standards
ELA
College and Career Readiness Anchor Standards for Writing
#7
Student promotes non-biased language in countering another
group’s perspective, based on his/her own personal experience.
Writing is clear and concise with the writer incorporating an
active voice.
Student writes in a crisp, clear, and succinct manner,
incorporating an active voice. Appropriate use of pronouns,
modifiers and non-biased language is evident.
Student writes in a generally clear, but unnecessary manner
where, non-biased language is occasionally used to produce
words that counter a group’s perspective. Sometimes the
meaning is obscured.
Student writes in an unclear manner, avoiding non-biased
language, and using inappropriate or inaccurate words that
often.
Student writes in a manner that does not adequately support the
assignment, making no effort to avoid non-biased language.
Common Core State Standards
ELA
27. College and Career Readiness Anchor Standards for Writing #7
Produce clear and coherent writing, with strong evidence of
being proofread, in which the development, organization, and
style are appropriate to task, purpose, and audience.
Student submits writing that is thoroughly proofread, with no
apparent errors.
Student submits writing that has been proofread in a cursory
manner (1 - 5 errors), but overall is unimpaired.
Student submits writing that has been poorly proofread (more
than 5 errors) that impair overall content.
Student submits writing that clearly has not been proofread,
rendering it unacceptable for graduate work.
Revised July 15, 2012