Measures of Central Tendency: Mean, Median and Mode
MTH 231 Entire Course Guide
1. MTH 231 Entire Course
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MTH 231 Week 1 DQs
MTH 231 Week 1 Populations and Sampling Paper
MTH 231 Week 2 DQs
MTH 231 Week 2 Data—Organizing, Summarizing, Probability, and
Distribution Worksheet
MTH 231 Week 3 DQs
MTH 231 Week 3 Life Sciences Article Analysis
MTH 231 Week 4 DQs
MTH 231 Week 4 Confidence Intervals in the Life Sciences
Presentation
MTH 231 Week 4 Distribution, Hypothesis Testing, and Error
Worksheet
MTH 231 Week 5 Final Exam
MTH 231 Week 5 Hypothesis Testing and Correlation Worksheet
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2. MTH 231 Final Exam Guide Set 2
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Use the following table for questions 1 and 2.
Butterflies
Red
Blue
Orange
4. 9
43
1. If you randomly select one butterfly from the table above, what
is the probability of selecting a red butterfly or one collected in
spring?
2. If you randomly select one butterfly collected in spring, one
butterfly collected in summer, and one butterfly collected in autumn,
what is the probability of selecting all yellow butterflies?
3. Determine the appropriate approach to conduct a hypothesis test
for this claim: Fewer than 5% of patients experience negative
treatment effects. Sample data: Of 500 randomly selected patients,
2.2% experience negative treatment effects.
A) Use the normal distribution.
B) Use the Student t distribution.
C) Use the chi-square distribution.
D) Use nonparametric or bootstrapping methods.
4. Determine the appropriate approach to conduct a hypothesis test
for this claim: The systolic blood pressure of men who run at least
five miles each week varies less than does the systolic blood pressure
of all men. Sample data: n = 100 randomly selected men who run at
least five miles each week, sample mean = 108.4, and s = 20.3
A) Use the normal distribution.
B) Use the Student t distribution.
C) Use the chi-square distribution.
D) Use nonparametric or bootstrapping methods.
5. Determine the appropriate approach to conduct a hypothesis test
for this claim: The mean sodium content of a 30 g serving of snack
crackers is 2,200 mg. Sample data: n = 130 snack crackers, sample
5. mean= 3,100 mg, and s = 570. The sample data appear to come from a
normally distributed population.
A) Use the normal distribution.
B) Use the Student t distribution.
C) Use the chi-square distribution.
D) Use nonparametric or bootstrapping methods.
Use the following sample data to answer questions 6 through 12.A
study of physical fitness tests for 12 randomly selected premedical
students measured their exercise capacity (in minutes). The following
data resulted:
25 61 23 22 24 53
33 31 23 23 63 71
6. Calculate the mean of the students’ exercise capacity.
7. Calculate the median of the students’ exercise capacity.
8. Calculate the mode of the students’ exercise capacity.
9. Calculate the standard deviation of the students’ exercise capacity.
10. Calculate a 90% Confidence Interval for the student's mean
exercise capacity.
11. If premedical student Alisha has the exercise capacity of 42
minutes, convert her score to a z score among the distribution of
exercise capacity above.
12. Alisha’s grandmother has an exercise capacity of 21 minutes, as
measured in a similar study among Americans over seventy years old.
The study sample has a mean of 15.2 minutes and a standard
deviation of 7.3 minutes. Convert Alisha’s grandmother’s score to a z
score among the distribution of exercise capacity in Americans over
6. seventy years old. Who has a relatively longer exercise capacity
compared to her peers—Alisha or her grandmother?
13. Choose the procedure that will allow dental patients to be
researched using a binomial distribution:
A) Surveying dental patients and asking them how their visit could
have been made more enjoyable
B) Asking dental patients as they enter the office how often they
floss
C) Surveying a set number of dental patients and asking them if
they have dental insurance
D) Asking patients as they enter the office whether they flossed
before the appointment
E) Surveying dental patients and asking them how their teeth feel
after their appointment
14. Select the procedure that results in a Poisson distribution and
explain.
F) Researching the Northern Spotted Owls' number of feedings per
month
G) Researching the Barred Owls' wingspan in inches
H) Researching the Snowy Owls' preferred nesting locations
I) Researching the Sooty Owls' longevity
15. Choose the procedure that will allow fire ants to be researched
using a Poisson distribution.
J) Counting fire ants per square centimeter of a mound
7. K) Counting fire ant mounds per square kilometer throughout
North America
L) Surveying 2,080 North Americans to determine how many fire
ant bites they have suffered in the past year
M) Surveying 2,080 North Americans to determine how they feel
about fire ants
N) Recording the locations of fire ant mounds each year in one
county over a span of 40 years
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MTH 231 Week 1 DQ 1 and DQ 2
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Week 1 DQ 1
Select the commodity of your best interest by ticking the box. You
should get the data table thru clicking "retrieve" button at the end part
of the list. ( You may use a commodity which is not explained in the
class)
Select the data among the month from 10 to 11 years as depicted
below. Paste it to your clipboard using your mouse. Use only the
numbers, not the month.
Apply statdisk and paste it on statdisk. You are then required to select
which column to be used. You have to choose column 1.
8. Week 1 DQ 2
There are two broad areas of statistics: inferential and descriptive. In
inferential statistics, we use analytical methods to derive meaning
from our data. In descriptive statistics, we study effective ways to
describe the data. Charts and graphs are very important in descriptive
statistics. Compare the graphs in Figures 2-6, 2-7, and 2-10 in the
text. What does each graph communicate? How effective is each
graph in communicating this information? How would you choose the
kind of graph to use for a specific project? Give an example
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MTH 231 Week 1 Individual Assignment
Populations and Sampling Paper
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Resources: Ch. 1 of the text, the Internet, and the University Library
Consider how life sciences researchers collect information from
samples to learn about populations.
Write a 700- to 1,050-word paper about sampling from populations.
Include the following information:
Define population and describe the characteristics of a population.
Define sample and describe the characteristics of a sample.
Compare samples and populations and explain how the concepts are
related. Provide examples to illustrate your arguments.
Explain how to increase the chance that a sample is representative of
a chosen population. Provide an example.
Describe random sampling and its benefits for research.
Cite at least two references.
9. Format your paper consistent with APA guidelines.
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MTH 231 Week 2 DQ 1 and DQ 2
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Week 2 DQ 1
Suppose a birdwatcher averages spotting 0.3 rare finches every day
during the two hours allotted for watching. This means that the
birdwatcher spots, on average, three rare finches every 10 days. The
average is based on considerable experience. Over a given 10-day
period, the birdwatcher sees zero rare finches in five days, and on the
sixth day, the birdwatcher declares, “I’m due to see a rare finch
today.”
Assume that the environmental conditions are reasonably constant
with no seasonal migratory issues involved. There is reasonably
consistent weather and there are no confounding (lurking, unseen)
variables involved. There is, however, a flaw in the birdwatcher’s
statement. What is the error and why is it wrong?
Would you choose the binomial pdf (probability distribution function)
or would you choose the Poisson pdf to better analyze the
birdwatcher's scenario (Triola, Sec. 4.3 & 4.4, 2006)? State the
necessary criteria for each distribution and support your decision.
Triola, M. M., Triola, M. D., &Triola, M. F. (2006). Biostatistics for
the biological and health sciences. Retrieved from The University of
Phoenix eBook Collection database.
Week 2 DQ 2
10. Read the article What are Relative Risk, Number Needed to Treat and
Odds Ratio? from the Electronic Reserve Readings on the Materials
web page for Week 2. Summarize the measures of relative risk,
number needed to treat, and odds ratios. In your opinion, which of
these measures is most informative? Why are they frequently used
together? Explain.
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MTH 231 Week 2 Individual Assignment Data-
Organizing, Summarizing, Probability, and
Distribution Worksheet
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Resources: Ch. 2–4 and Appendix B of the text and Statdisk
Complete the University of Phoenix Material: Data—Organizing,
Summarizing, Probability, and Distribution Worksheet located in
Week Two of the student website (Materials web page).
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MTH 231 Week 3 DQ 1 and DQ 2
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11. Week 3 DQ 1
What are the characteristics of a normal probability distribution
function (pdf).
What is the standard normal pdf? How is it related to the normal pdf
and why is it useful?
Explain the Empirical Rule? Is it used for rough estimates or precise
calculations?
Briefly tell how to use Table A-2 in the Appendix of our text to
calculate z-values (Triola, 2006). How is area under the standard
normal curve related to probability? Is the table arranged so that
probability is cumulative from the left or from the right?
Briefly tell how Statdisk may be used to give even more accurate
table values (Statdisk>> Analysis >> Probability Distributions >>
Normal Distribution).
Week 3 DQ 2
Precisely, in simple language, what is a confidence interval?
What is the difference between a statistic that is a point estimator and
one that is an interval estimator? When might you prefer an interval
estimator over a point estimator?
What is a confidence level with respect to a confidence interval?
What is a critical value and why is it important?
12. What happens to the margin of error for a confidence interval when
the sample size is increased? How is the margin of error related to the
width of the confidence interval? State this relationship in
mathematical terms.
What happens to the width of the confidence interval if the confidence
level is increased from 95% to 99%? That is, does the width increase
or decrease? Why?
What happens to the width of the confidence interval if n, the size of
the sample, is increased? Why?
For additional participation credit, also comment within the thread of
the message posted in the Main Forum: Example: Using Statdisk to
Find a Confidence Interval
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MTH 231 Week 3 Team Assignment Life
Sciences Article Analysis
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Resources: Ch. 3 and 4 of the text, the Week Two Electronic
Reserve Readings “Fetal Deaths and Proximity to Hazardous Waste
Sites in Washington State” and “Intensive Lipid Lowering With
Atorvastatin in Patients With Coronary Artery Disease, Diabetes, and
Chronic Kidney Disease,” the Internet, and the University Library
Discuss the methodology of life sciences researchers in the two
articles. Explore the data collection and analysis techniques used by
13. the authors of these articles in preparation for the Life Sciences
Article Analysis.
Write a 1,050- to 1,750-word paper about dependence and
probability. Discuss the following questions:
What population is researched in each article?
What data are collected by the authors in each article? What are the
independent events or variables? What are the dependent events or
variables? Evaluate whether the authors make appropriate claims
related to the independence or dependence of the events or variables
they investigate.
Explain relative risk, odds ratios, and fetal death rates. Describe the
use of these tools in the article “Fetal Deaths and Proximity to
Hazardous Waste Sites in Washington State.”
Explain absolute risk reduction and number needed to treat.
Describe the use of these tools in the article “Intensive Lipid
Lowering With Atorvastatin in Patients With Coronary Artery
Disease, Diabetes, and Chronic Kidney Disease.”
Summarize how communication of scientific findings is facilitated
with the concept of dependence and with tools for expressing
probability.
Cite at least four references.
Format your paper consistent with APA guidelines.
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MTH 231 Week 4 DQ 1 and DQ 2
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Week 4 DQ 1
14. State the criteria for choosing a t-test and a z-test. Then give an
example of a problem in which you would use z-test to evaluate the
data. Next, take the same example and modify it so that a t-test would
be preferable. Explain why.
Week 4 DQ 2
In general terms:
· What is a null hypothesis?
· What is an alternative hypothesis?
Under American criminal jurisprudence, the accused is presumed
innocent until proven guilty beyond the “shadow of a doubt.”
· What is the null hypothesis?
· What is the alternative hypothesis?
· Explain how the Type I and Type II errors apply to the court system.
· In court, what is the equivalent of the test statistic upon which the
decision is based?
· In statistical terms, how would you define “shadow of a doubt?”
· In statistics, why should the decision always be stated in terms of the
null hypothesis? (That is: reject the null hypothesis or fail to reject the
null hypothesis.)
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MTH 231 Week 4 Individual Assignment
Distribution, Hypothesis Testing, and Error
Worksheet
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Resources: Ch. 5–7 of the text and Statdisk
15. Complete the University of Phoenix Material: Distribution,
Hypothesis Testing, and Error Worksheet, located in Week Four of
the student website.
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MTH 231 Week 4 Team Assignment Confidence
Intervals in the Life Sciences Presentation
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Resources: Ch. 5 and 6 of the text, the University Library, the
Internet, and Statdisk
Identify a normally distributed variable related to your chosen life
science that serves as your example variable. Review the data sets
presented in Appendix B of the text and in Statdisk, selecting one that
corresponds with your chosen life science. Choose a particular
variable you would like to explore and use Statdisk to determine if its
distribution is approximately normal.
Note. Data Set 5: Passive and Active Smoke in the text does not
include normally distributed data and may not be used in this project.
Prepare a 12- to 15-slide Microsoft® PowerPoint® presentation that
explains confidence intervals in your chosen life science. Imagine that
you are responsible for educating first-year college students who are
majoring in your chosen life science. Explain to the students how and
why confidence intervals relate to their field.
Discuss the following questions:
What is a normal distribution? Describe your example variable and
explain why normally distributed data is important in your chosen life
science. Show the distribution of your example variable in a Statdisk-
16. generated image and demonstrate how to calculate the probability of a
range of values within this normal distribution.
What is a standard normal distribution? How does it differ from other
normal distributions? Convert the normally distributed example
variable within your chosen life science to a standard normal
distribution. Show this example in a Statdisk-generated image and
demonstrate how to calculate the probability of a range of values
within this standard normal distribution.
What is a confidence interval? Outline how confidence intervals may
be used in your chosen life science. Demonstrate how to define
confidence intervals within the normal distribution example variable.
What is a confidence level? Show how a confidence level relates to
the confidence interval using the example variable.
What is a critical value? Show how critical values relate to the
confidence interval using the example variable.
What is a margin of error? Describe how a margin of error relates to
confidence intervals and to your chosen life science.
Provide an example related to your example variable.
What is a point estimate? Explain how a point estimate found from a
confidence interval would be applied in your chosen life science.
Provide an example related to your example variable.
What can a confidence interval tell researchers in your chosen life
science about an estimate of population mean? Provide an example
related to your example variable.
What can a confidence interval tell researchers in your chosen life
science about an estimate of population variance? Provide an example
related to your example variable.
Include a title slide and conclusion slide, and cite at least four
references on a references slide.
Present the information about confidence intervals and your chosen
life science to the instructor and the class just as you would to first
year college students who need this information.
For Local Campus students, these are oral presentations accompanied
by Microsoft® PowerPoint® presentations.
For Online and Directed Study students, these are Microsoft®
PowerPoint® presentations with notes.
Discuss with your classmates and answer questions
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MTH 231 Week 5 Final Exam Guide
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We have another set of MTH 231 Final, which could be found on this
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MTH 231 Week 5 Final Exam
Use this worksheet for your answers. Your score, based on the points
shown for this exam in the rubric, will be corrected to the basis points
shown for the final exam in the syllabus. Submit to the Assignments
Section by 11:59 pm of the last day of class. Late work will not be
accepted.
1. The following are the scores obtained by 30 students in
epidemiology test:
83 67 94 77 55 82
79 72 88 65 81 63
92 61 85 71 79 70
89 52 66 63 75 84
99 81 73 79 68 77
a) Apply the Statdisk and look for the user-defined relative
frequency histogram having a class width of 10 from 50. The labels
must be “on”. Copy the histogram in this sheet.
18. b) Look for the Normality Assessment using the Statdisk.
Does it show the sample from the normal population?
Are the results from the histogram and the test results the same with
regard to normality?
What did you apply for the alpha level of the test? 0
c) Refer to the Statdisk, get the descriptive statistics of the data
below:
Mean
Median
Standard Deviation
Range
Midrange
d) Sarah got 79 in her exam. The z-score is shown below:
0.2927
2. The die rolled once with the events as shown:
A: Event F: Roll an even number
B: Event J: Roll 1, 2, 3, or 4
a) Define the term mutually exclusive.
There are two events which are independent and the existence of the
first event has nothing to do with the existence of another.
b) What set has mutually exclusive events? A, B, Both, or
Neither?
A
3. Every person at St. Goodenough Hospital is categorized as
below average, average, or above average with regard to the
understanding. They are also divided as fair, good, or excellent. The
evaluation is shown below:
----Potential for Advancement----
Prof. Knowledge Fair Good Excellent
Below Average 16 12 22
Average 45 60 45
Above Average 93 72 135
a) Get the probability of the chosen employee at random having
the excellent potential advancement.
b) Get the probability of the person being selected at random
who is having an average or above average professional knowledge,
as well as excellent potential advancement.
19. 4. Correctly, what is the Central Limit Theorem (CLT)? Explain
in full detail why is it essential?
1) When the samples of size of at least 30 came from random
population, then the sampling distribution have an estimated normal
distribution;
2) If the population is distributed accordingly, then the sampling
distribution have a normal distribution as well.
3) For any kind of sample size, the population is normally
distributed.
4) This is beyond the result of CLT, than the accurate statement
of it.
The CLT is essential because it provides the sampling distribution of
the sample means.
5. Indicate whether each statement is valid with a “Yes” or “No.”
a. Under particular limitations, the binomial distribution can be
estimate by the normal distribution allowing us to apply the normal
distribution for computation with the binomial distribution.
b. As what has been stated in CLT, the sampling distribution of
the sampling mean estimates the normal distribution in a manner that
it may not enhance the size of the given samples.
c. The CLT may not be used until the population probability
distribution become identifiable.
d. No proof was used in CLT. It still a hypothesis
6. The post anaesthesia care area (recovery room) at St. Luke’s
Hospital in Pflugerville, Ontario, was broadened. The move will mean
that the mean number of people per day can also be enlarged. A
random sampling was conducted in order to determine the patients
coming after the broadening.
25 27 25 26 25 28 28 27 24 26 25 29 25 27 24
a What is the null hypothesis? The mean number of patients
per day arrived to be 25 or less.
b What is the alternative hypothesis? The mean number of
patients per day will be greater than 25
c What specific test will you use to test the hypotheses at α =
0.05? t-test
d What is the p-value for the test? p = 0.0087
20. e Interpret the meaning of this p-value. The probability of
arriving with the test statistics is 2.6935 if the null hypothesis holds to
be true. This is the value used in t-statistic excluding the null
hypothesis.
f What is the critical value for the test? (Assume α = 0.05.)
cv = 1.7613
g Interpret the meaning of this critical value. If we like to
manipulate the type I error to become 0.05 or lesser, then the greatest
value for the test should be1.7613.
There must be more explanation here.
h Is there sufficient statistical evidence at the 0.05 significance
level to reject the null hypothesis? Yes, because the p-value is less
than 0.05.
i Is this a right-tail test, left-tail test, or two-tail test? Right-tail
test
7 Choose one best answer among the given options.
a) There are a lot of values
b) A range of values is formulated from the given data in order to
present the parameyers inside the range at a particular probability: a
confidence interval
(1) the population parameter
(2) a point estimate
(3) the mean of the population
c) What affects the sample error aside from the standard
deviation? a confidence interval
(1) the population parameter
(2) the point estimate
(3) the sample size
d) For example, you have 100 sample population, for every
sample you establish 95% confidence interval for the mean. WE are
right to assume that 95% of the confidence interval is one of the
following:
(1) a sample mean
(2) the population mean
(3) a point estimate
(4) the standard deviation of the population
21. e) The t-distribution is applied if the population has one of the
following aside from having a normal distribution:
(1) the population standard deviation is unknown
(2) the population standard deviation is known
(3) the mean of the population is unknown
(4) the point estimate is known
8 As part of the protocol, the Keystone Police selected 65
ambulances and inspect their tires. The sample mean for this was 32
32 lbs/sq. in. While the standard deviation was 2lbs/sq. in. Get the
98% confidence interval of said population. You may refer to
Statdisk.
a Confidence Interval:
b Margin of Error:
c With a larger sample size, would you expect the margin of
error to increase or decrease?
9 Get the right and precise response for the following:
a) Define correlation analysis
b) In what manner that the dependent variable in correlation is
being determined? What is the other term for it?
c) In what manner that the dependent variable in correlation is
being determined? What is the other term for it?
Based on the study, the independent variable pertains to the value that
can changed and controlled by the research. It is assumable variable
in the research.
d) Is there causality present on both variables? Explain
The relationship of the two variables does not indicate any causality,
it only suggests that there is a linear relationship existing in both
variables, but does not show any kind of causality.
10 Look for the incorrect portion among the statements below
about the coefficient of correlation
a) It can cover from -1 to +1.
b) The square is the coefficient of identification.
c) It pertains to the rate of variation discussed.
d) It is a shows the relationship between two variables.
11 A research was formulated about the automobile speeds of a
particular model and the outcome fuel consumption rank. Think that
22. the data provided below was randomly gathered. Refer to the Statdisk
in order to answer the statements below.
a. Calculate the coefficient thru the Statdisk
b. Explain the outcome of your computation
Speed MPG
45 33
52 32
49 28
60 26
67 22
61 21
a What is the coefficient or correlation and interpret and define
it as well r = -0.877
b What is the coefficient of determination and describe it as
well. r2 = 0.769
c Identify the relationship of speed and mpg in layman’s term
referring to the result of your computation. It suggests that there is a
negative correlation exiting on speed and mpg
d What statistic should we use in order to get the variance?
76.9% of can be explained by the regression model.
12 Immediately after the 9-11 incident, America Online
conducted a survey about: the reestablishment of World Trade Center.
The responses are the following:
Yes - 768,731
No -286,756
Too soon to decide
The respondents who participate is of large number, is it the
representation of the entire US population?
13 What level of measurement should be used on the following:
(nominal, ordinal, interval, ratio)
a) The weight of the airplane passengers
b) How the doctor describe the following: “abstains from
alcohol, light drinker, moderate drinker, heavy drinker”
¬¬¬¬¬¬¬¬¬¬¬¬¬¬
c) The questions about the emotions of people during the day
ranging from 1-10 scale
d) The following colors: red, blue, white, tan, black, yellow
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MTH 231 Week 5 Team Assignment Hypothesis
Testing and Correlation Worksheet
For more classes visit
www.snaptutorial.com
Resources: Ch. 7 and 8 and sections 9-1 and 9-2 in Ch. 9 of the text
Complete the University of Phoenix Material: Hypothesis Testing and
Correlation Worksheet, located in Week Five of the student website.
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