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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.
DeVry MATH221 Week 2 Discussion Latest 2016 November
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.
DeVry MATH221 Week 3 Discussion Latest 2016 November

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
DeVry MATH221 Week 4 Discussion Latest 2016 November

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.

DeVry MATH221 Week 5 Discussion Latest 2016 November

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.
DeVry MATH221 Week 6 Discussion Latest 2016 November

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.
DeVry MATH221 Week 7 Discussion Latest 2016 November

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

DeVry MATH221 Week 4 iLab Latest 2016 November

MATH 221 Statistics for Decision Making
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 =:

6. Calculate (by hand) the mean and standard deviation for the binomial distribution with the 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:
Standard Deviation =:
Comparison:

7. Calculate (by hand) the mean and standard deviation for the binomial distribution with the 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:
Standard Deviation =:
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:

DeVry MATH221 Week 6 iLab Latest 2016 November

MATH 221 Statistics for Decision Making
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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DeVry MATH 221 All Discussion+ilbs-Latest 2016 November 1