De vry math 221 all discussion+ilbs latest 2016 november

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DeVry MATH 221 All Discussion+ilbs-Latest 2016
November
Question
DeVry MATH221 Week 1 Discussion Latest 2016 November
There are lots of "helps" available in this course. Please find one and tell us why it will be useful
for you.
Then give careful directions for how to find that "help."
Be sure to look in the left hand navigation area and also on the upper toolbar as well as in MSL.
Try to find one which hasn't already been mentioned.
A regression equation can be graphed. The graph will go uphill as we look at it going from the
left to the right; or it will go downhill as we look at it going from the left to the right; or it will be
parallel to the x-axis.
Take a look at several examples in the text or in the Homework and ponder for awhile.
Then write a very short idea about what's going on with correlation (consider the r-value), with
slope, and anything else you might notice.
Rather than being redundant, please read the ideas your classmates post and comment or add to
what they observed.
Probability and Odds (graded)
Please watch for a new question each day. Please post 3 times minimum.
And be sure to follow the post on 3 different days requirement as well as the 1st post before
midnight Wednesday requirement
Discrete Probability Variables (graded)
There will be a new question each day. Be sure to post on 3 different days.
If I can count it, then it's discrete. If I can measure it, then it's continuous.
Please keep these 2 statements in mind as we study random variables.
For today's post please give an example of a discrete random variable.
eg.

If I have 8 cans of coca cola in my refrigerator, that's a discrete random variable --- I can count
them.
But, if I say that I have 12 ounces in each can, that's continuous because that's a measurement.
And I can't really say that it's 12 ounces. It might be 12. 1 or 11.9 or it could even be 12.05 or
11.95. Getting more accurate it could be 12.00001 or 11.99999. And that's why we call it
continuous --- on the number line I can always get a little closer than I was a moment ago.
Interpreting Normal Distributions (graded)
Please look for a new question each day. Please post on 3 different days.
A skill which will be tremendously important in the coming weeks is sketching a normal curve.
And to sketch it we need to draw the x-axis accurately.
Here's one for a curve when the mean is 0 and the standard deviation is 1.
_____-3_____-2_____-1_____*0*_____+1_____+2_____+3_____
And here's one for a curve when the mean is 40 and the standard deviation is 4.
_____28_____32_____36____*40*____44_____48_____52_____
And here's another for a curve when the mean is 10 and the standard deviation is 6.
_____-8_____-2_____+4_____*10*_____16_____22_____28_____
For today's post please find a normal distribution in the text or in MSL and sketch the
appropriate x-axis.
Confidence Interval Concepts (graded)
Please watch for a new question each day. Be sure to post on 3 different days.
There are many online calculators for confidence intervals.
Find one. Use it. Compare your answer with an answer from one of the examples in the book
(that way you'll know if it is correct). Then share the URL with us and talk about how easy or
hard it is to use.
Rejection Region (graded)
Please watch for a new question each day. Be sure to post on 3 different days.
How is the rejection region defined, and how is that related to the p value?
DeVry MATH221 Week 2 iLab Latest 2016
November

MATH 221 Statistics for Decision Making
Week 2 iLab
Name:_______________________
Statistical Concepts that you will learn after completing this iLab:
· Using Excel for Statistics
· Graphics
· Shapes of Distributions
· Descriptive Statistics
· Empirical Rule
Week 2 iLab Instructions-BEGIN
Ø Data have already been formatted and entered into an Excelworksheet.
Ø Obtain the data file for this lab from your instructor.
Ø The names of each variable from the survey are in the first row of the Worksheet. This row has
a background color of gray to identify it as the variable names. All other rows of the Worksheet
represent a certain students’ answers to the survey questions. Therefore, the rows are called
observations and the columns are called variables. On page 6 of this lab, you will find a code
sheetthat identifies the correspondence between the variable names and the survey questions.
Ø Follow the directions below and then paste the graphs from Excel in the grey areas for
question 1 through 3. Type your answers to questions 4 through 11 where noted in the grey
areas. When asked for explanations, please give thorough, multi-sentence or paragraph length
explanations.
Ø PLEASE NOTE that various versions of Excel may have slightly different formula commands.
For example, some versions use =STDEV.S while other versions would use =STDEVS (without
the dot before the last “S”).
Ø The completed iLab Word Document with your responses to the 11 questions will be the ONE
and only document submitted to the dropbox. When saving and submitting the document, you
are required to use the following format: Last Name_ First Name_Week2iLab.
Week 2 iLab Instructions-END
Creating Graphs
1. Create a piechart for the variable Car Color: Select the column with the Car variable, including
the title of Car Color. Click onInsert, and thenRecommended Charts. It should show a
clustered column and clickOK. Once the chart is shown, right click on the chart (main area) and
selectChange Chart Type. SelectPieandOK. Click on the pie slices, right clickAdd Data
Labels, and selectAdd Data Callouts. Add an appropriate title.Copy and paste the chart here. (4
points)
2. Create a histogram for the variable Height.You need to create a frequency distribution for the
data by hand. Use 5 classes, find the class width, and then create the classes. Once you have the
classes, count how many data points fall within each class.It may be helpful to sort the data
based on theHeightvariable first. Create a new worksheet in Excel by clicking on the + along the

bottom of the screen and type in the categories and the frequency for each category. Then select
the frequency table, click onInsert, thenRecommended Chartsand choose the column chart
shown and clickOK. Right click on one of the bars and selectFormat Data Series. In the pop up
box, change theGap Widthto 0. Add an appropriate title and axis label.Copy and paste the graph
here. (4 points)
3. Type up a stem-and-leaf plot chart in the box below for the variable Money, with a space
between the stems and the group of leaves in each line. Use the tens value as the stem and the
ones value for the leaves. It may be helpful to sort the data based on the Money variable first.
An example of a stem-and-leaf plot would look like this:
0 4 5 6 9 3
1 5 6 3 6
2 9 2
The stem-and-leaf plot shown above would be for data 4, 5, 6, 9, 3, 15, 16, 13, 16, 29, and 22. (4
points)
Calculating Descriptive Statistics
4. Calculate descriptive statistics for the variable Height by Gender. Click onInsertand thenPivot
Table. Click in the top box and select all the data (including labels) fromHeightthroughGender.
Also click on “new worksheet” and thenOK. On the right of the new sheet, click
onHeightandGender, making sure thatGenderis in theRowsbox andHeightis in theValuesbox.
Click on the down arrow next toHeightin theValuesbox and selectValue Field Settings. In the
pop up box, clickAveragethenOK. Type in the averages below. Then click on the down arrow
next toHeightin theValuesbox again and selectValue Field Settings. In the pop up box, click
onStdDevthenOK. Type the standard deviations below. (3 points)
Mean Standard deviation
Females
Males
Short Answer Writing Assignment
All answers should be complete sentences.
5. What is the most common color of car for students who participated in this survey? Explain
how you arrived at your answer. (5 points)
1. What is seen in the histogram created for the heights of students in this class (include the
shape)? Explain your answer. (5 points)
1. What is seen in the stem and leaf plot for the money variable (include the shape)? Explain
your answer. (5 points)
1. Compare the mean for the heights of males and the mean for the heights of females in these
data. Compare the values and explain what can be concluded based on the numbers. (5 points)

1. Compare the standard deviation for the heights of males and the standard deviation for the
heights of females in the class. Compare the values and explain what can be concluded based on
the numbers. (5 points)
1. Using the empirical rule, 95% of female heights should be between what two values? Either
show work or explain how your answer was calculated. (5 points)
1. Using the empirical rule, 68% of male heights should be between what two values? Either
show work or explain how your answer was calculated. (5 points)
Code Sheet
DoNOTanswer these questions.
The Code Sheet just lists the variables name and the question used by the researchers on the
survey instrument that produced the data that are included in thedata file. This is just
information. The first question for the lab is after the code sheet.
Variable
Name Question
Drive
Question 1 – How long does it take you to drive to the school on average (to the
nearest minute)?
State Question 2 – What state/country were you born?
Temp Question 3 – What is the temperature outside right now?
Rank
Question 4 – Rank all of the courses you are currently taking. The class you look
most forward to taking will be ranked one, next two, and so on. What is the rank
assigned to this class?
Height Question 5 – What is your height to the nearest inch?
Shoe Question 6 – What is your shoe size?
Sleep Question 7 – How many hours did you sleep last night?
Gender Question 8 – What is your gender?
Race Question 9 – What is your race?
Car Question 10 – What color of car do you drive?
TV Question 11 – How long (on average) do you spend a day watching TV?
Money Question 12 – How much money do you have with you right now?
Coin Question 13 – Flip a coin 10 times. How many times did you get tails?
Die1 Question 14 – Roll a six-sided die 10 times and record the results.
Die2
Die3
Die4
Die5
Die6
Die7
Die8
Die9
Die10

November
Week 4 iLab
Name: _______________________
MATH221
Statistical Concepts:
· Probability
· Binomial Probability Distribution
Calculating Binomial Probabilities
Ø Open a new Excelworksheet.
1. Open spreadsheet
2. In cell A1 type “success” as the label
3. Under that in column A, type 0 through 10 (these will be in rows 2 through 12)
4. In cell B1, type “one fourth”
5. In cell B2, type “=BINOM.DIST(A2,10,0.25,FALSE)” [NOTE: if you have Excel 2007, then
the formula is BINOMDIST without the period]
6. Then copy and paste this formula in cells B3 through B12
7. In cell C1, type “one half”
8. In cell C2, type “=BINOM.DIST(A2,10,0.5,FALSE)”
9. Copy and paste this formula in cells C3 through C12
10. In cell D1 type “three fourths”
11. In cell D2, type “=BINOM.DIST(A2,10,0.75,FALSE)”
12. Copy and paste this formula in cells D3 through D12
Plotting the Binomial Probabilities
1. Create plots for the three binomial distributions above. You can create the scatter plots in
Excel by selecting the data you want plotted, clicking on INSERT, CHARTS, SCATTER, then
selectingthe first chart shown which is dots with no connecting lines.Do this two more times and
for graph 2 set Y equal to ‘one half’ and X to ‘success’, and for graph 3 set Y equal to ‘three
fourths’ and X to ‘success’. Paste those three scatter plots in the grey area below. (9 points)
Calculating Descriptive Statistics

Ø You will use the same class survey results that were entered into the worksheet for the Week 2
iLab Assignment for question 2.
2. Calculate descriptive statistics for the variable(Coin) where each of the thirty-fivestudents
flipped a coin 10 times. Round your answers to three decimal places and typethe mean and the
standard deviation in the grey area below. (5 points)
Mean:
Standard deviation:
Short Answer Writing Assignment – Both the calculated binomial probabilities and the
descriptive statistics from the class database will be used to answer the following questions.
Round all numeric answers to three decimal places.
3. List the probability value for each possibility in the binomial experimentcalculated at the
beginning of this lab, which was calculated with the probability of a success being ½. (Complete
sentence not necessary; round your answers to three decimal places) (8 points)
P(x=0) P(x=6)
P(x=1) P(x=7)
P(x=2) P(x=8)
P(x=3) P(x=9)
P(x=4) P(x=10)
P(x=5)
4. Give the probability for the following based on the calculationsin question 3 above, with the
probability of a success being ½. (Complete sentence not necessary; round your answers to three
decimal places) (8 points)
P(x?1) P(x<0)
P(x>1) P(x?4)
P(4<x ?7) P(x<4 or x?7)
5. Calculate (by hand) the mean and standard deviation for the binomial distribution with the
probability of a success being ½and n = 10. Either show work or explain how your answer was
calculated. Use these formulas to do the hand calculations: Mean =np, Standard Deviation = (4
points)
Mean =np:
Standard Deviation =:
probability of a success being ¼ and n = 10. Write a comparison of these statistics to those from
question 5in a short paragraph of several complete sentences. Use these formulas to do the hand
calculations: Mean =np, Standard Deviation =(4 points)
Mean =np:
Comparison:
probability of a success being ¾and n = 10. Write a comparison of these statistics to those from
question 6in a short paragraph of several complete sentences. Use these formulas to do the hand
calculations: Mean =np, Standard Deviation =(4 points)

Mean =np:
Comparison:
8. Using all four of the properties of a Binomial experiment (see page 201 in the textbook)
explain in a short paragraph of several complete sentences why the Coin variable from the class
survey represents a binomial distribution from a binomial experiment. (4 points)
9. Compare the mean and standard deviation for the Coin variable (question 2) with those of the
mean and standard deviation for the binomial distribution that was calculated by hand in question
5. Explain how they are related in a short paragraph of several complete sentences. (4 points)
Mean from question #2:
Standard deviation from question #2:
Mean from question #5:
Standard deviation from question #5:
Comparison and explanation:
November
Week 6 iLab
Name:_______________________
Statistical Concepts:
· Data Simulation
· Confidence Intervals
· Normal Probabilities
Short Answer Writing Assignment
All answers should be complete sentences.
We need to find the confidence interval for the SLEEP variable. To do this, we need to find the
mean and then find the maximum error. Then we can use a calculator to find the interval, (x – E,
x + E).
First, find the mean. Under that column, in cell E37, type=AVERAGE(E2:E36). Under that in
cell E38, type=STDEV(E2:E36). Now we can find the maximum error of the confidence
interval. To find the maximum error, we use the “confidence” formula. In cell E39,
type=CONFIDENCE.NORM(0.05,E38,35). The 0.05 is based on the confidence level of 95%,
the E38 is the standard deviation, and 35 is the number in our sample. You then need to calculate
the confidence interval by using a calculator to subtractthe maximum error from the mean (x-E)
and add it to the mean (x+E).
1. Give and interpret the 95% confidence interval for the hours of sleep a student gets. (5 points)

Then, you can go down to cell E40 and type=CONFIDENCE.NORM(0.01,E38,35)to find the
maximum error for a 99% confidence interval. Again, you would need to use a calculator to
subtract this and add this to the mean to find the actual confidence interval.
2. Give and interpret the 99% confidence interval for the hours of sleep a student gets. (5 points)
3. Compare the 95% and 99% confidence intervals for the hours of sleep a student gets. Explain
the difference between these intervals and why this difference occurs. (5 points)
In the week 2 lab, you found the mean and the standard deviation for the HEIGHT variable for
both males and females. Use those values for follow these directions to calculate the numbers
again.
(From week 2 lab: Calculate descriptive statistics for the variable Height by Gender. Click
onInsertand thenPivot Table. Click in the top box and select all the data (including labels)
fromHeightthroughGender. Also click on “new worksheet” and thenOK. On the right of the
new sheet, click onHeightandGender, making sure thatGenderis in theRowsbox andHeightis in
theValuesbox. Click on the down arrow next toHeightin theValuesbox and selectValue Field
Settings. In the pop up box, clickAveragethenOK. Write these down. Then click on the down
arrow next toHeightin theValuesbox again and selectValue Field Settings. In the pop up box,
click onStdDevthenOK. Write these values down.)
You will also need the number of males and the number of females in the dataset. You can either
use the same pivot table created above by selectingCountin theValue Field Settings, or you can
actually count in the dataset.
Then in Excel (somewhere on the data file or in a blank worksheet), calculate the maximum error
for the females and the maximum error for the males. To find the maximum error for the
females, type=CONFIDENCE.T(0.05,stdev,#), using the females’ height standard deviation for
“stdev” in the formula and the number of females in your sample for the “#”. Then you can use a
calculator to add and subtract this maximum error from the average female height for the 95%
confidence interval. Do this again with 0.01 as the alpha in the beginning of the formula to find
the 99% confidence interval.
Find these same two intervals for the male data by using the same formula, but using the males’
standard deviation for “stdev” and the number of males in your sample for the “#”.
4. Give and interpret the 95% confidence intervals for males and females on the HEIGHT
variable. Which is wider and why? (7 points)
5. Give and interpret the 99% confidence intervals for males and females on the HEIGHT
variable. Which is wider and why? (7 points)
6. Find the mean and standard deviation of the DRIVE variable by
using=AVERAGE(A2:A36)and=STDEV(A2:A36). Assuming that this variable is normally
distributed, what percentage of data would you predict would be less than 40 miles? This would
be based on the calculated probability. Use the formula=NORM.DIST(40, mean, stdev,TRUE).
Now determine the percentage of data points in the dataset that fall within this range. To find the
actual percentage in the dataset, sort the DRIVE variable and count how many of the data points
are less than 40 out of the total 35 data points. That is the actual percentage. How does this
compare with your prediction? (10 points)
Mean ______________ Standard deviation ____________________

Predicted percentage ______________________________
Actual percentage _____________________________
Comparison ___________________________________________________
______________________________________________________________
7. What percentage of data would you predict would be between 40 and 70 and what percentage
would you predict would be more than 70 miles? Subtract the probabilities found
through=NORM.DIST(70, mean, stdev, TRUE)and=NORM.DIST(40, mean, stdev,
TRUE)for the “between” probability. To get the probability of over 70, use the
same=NORM.DIST(70, mean, stdev, TRUE)and then subtract the result from 1 to get “more
than”. Now determine the percentage of data points in the dataset that fall within this range,
using same strategy as above for counting data points in the data set. How do each of these
compare with your prediction and why is there a difference? (11points)
Predicted percentage between 40 and 70 ______________________________
Actual percentage _____________________________________________
Predicted percentage more than 70 miles ________________________________
Actual percentage ___________________________________________
Comparison ____________________________________________________
_______________________________________________________________
Why? __________________________________________________________
________________________________________________________________
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