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**MATH533 DeVry University - Course Project AJ DAVIS - Complete Solution**

- From Mathematics, Statistics

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**Course Project: AJ DAVIS DEPARTMENT STORES**

Introduction

AJ DAVIS is a department store chain, which has many credit customers and wants to find out

more information about these customers. A sample of 50 credit customers is selected with data

collected on the following five variables.

1. Location (rural, urban, suburban)

2. Income (in $1,000'sbe careful with this)

3. Size (household size, meaning number of people living in the household)

4. Years (the number of years that the customer has lived in the current location)

5. Credit balance (the customers current credit card balance on the store's credit card, in $).

The data is available in Doc Sharing Course Project Data Set as an Excel file. You are to copy

and paste the data set into a minitab worksheet.

**PROJECT PART A: Exploratory Data Analysis**

Open the file MATH533 Project Consumer.xls from the Course Project Data Set folder in

Doc Sharing.

For each of the five variables, process, organize, present, and summarize the data.

Analyze each variable by itself using graphical and numerical techniques of

summarization. Use minitab as much as possible, explaining what the printout tells you.

You may wish to use some of the following graphs: stem-leaf diagram, frequency or

relative frequency table, histogram, boxplot, dotplot, pie chart, bar graph. Caution: Not all

of these are appropriate for each of these variables, nor are they all necessary. More is

not necessarily better. In addition, be sure to find the appropriate measures of central

tendency and measures of dispersion for the above data. Where appropriate use the five

number summary (the Min, Q1, Median, Q3, Max). Once again, use minitab as

appropriate, and explain what the results mean.

Analyze the connections or relationships between the variables. There are 10 pairings

here (location and income, location and size, location and years, location and credit

balance, income and size, income and years, income and balance, size and years, size

and credit balance, years and Credit Balance). Use graphical as well as numerical

summary measures. Explain what you see. Be sure to consider all 10 pairings. Some

variables show clear relationships, while others do not.

Prepare your report in Microsoft Word (or some other word processing package),

integrating your graphs and tables with text explanations and interpretations. Be sure that

you have graphical and numerical back up for your explanations and interpretations. Be

selective in what you include in the report. I'm not looking for a 20-page report on every

variable and every possible relationship (that's 15 things to do). Rather, what I want you

do is to highlight what you see for three individual variables (no more than one graph for

each, one or two measures of central tendency and variability (as appropriate), and two

or three sentences of interpretation). For the 10 pairings, identify and report only on three

of the pairings, again using graphical and numerical summary (as appropriate), with

interpretations. Please note that at least one of your pairings must include location and at

least one of your pairings must not include location.

All DeVry University policies are in effect, including the plagiarism policy.

Project Part A report is due by the end of Week 2.

Project Part A is worth 100 total points. See grading rubric below.

Submission: The report from Part 4, including all relevant graphs and numerical analysis along

with interpretations

Format for report:

A. Brief introduction

B. Discuss your first individual variable, using graphical, numerical summary, and

interpretation

C. Discuss your second individual variable, using graphical, numerical summary, and

interpretation

D. Discuss your third individual variable, using graphical, numerical summary, and

interpretation

E. Discuss your first pairing of variables, using graphical, numerical summary, and

interpretation

F. Discuss your second pairing of variables, using graphical, numerical summary, and

interpretation

G. Discuss your third pairing of variables, using graphical, numerical summary, and

interpretation

H. Conclusion**Project Part B: Hypothesis Testing and Confidence**

Intervals

Your manager has speculated the following.

a. The average (mean) annual income was greater than $45,000.

b. The true population proportion of customers who live in a suburban area is less than 45%.

c. The average (mean) number of years lived in the current home is greater than 8 years.

d. The average (mean) credit balance for rural customers is less than $3,200.

1. Using the sample data, perform the hypothesis test for each of the above situations in

order to see if there is evidence to support your managers belief in each case AD. In

each case, use the Seven Elements of a Test of Hypothesis in Section 6.2 of your text

book with = .05, and explain your conclusion in simple terms. Also, be sure to compute

the p-value and interpret.

2. Follow this up with computing 95% confidence intervals for each of the variables

described in AD, and again interpreting these intervals.

3. Write a report to your manager about the results, distilling down the results in a way that

would be understandable to someone who does not know statistics. Clear explanations

and interpretations are critical.

4. All DeVry University policies are in effect, including the plagiarism policy.

5. Project Part B report is due by the end of Week 6.

6. Project Part B is worth 100 total points. See the grading rubric below.

Submission: The report from Part 3 and all of the relevant work done in the hypothesis testing

(including minitab) in 1 and the confidence intervals (minitab) in Part 2 as an appendix

Format for report:

A. Summary report (about one paragraph on each of the speculations, AD)

B. Appendix with all of the steps in hypothesis testing (the format of the Seven Elements of

a Test of Hypothesis, in Section 6.2 of your text book) for each speculation AD, as well

as the confidence intervals, including all minitab output**Project Part C: Regression and Correlation Analysis**

Using MINITAB, perform the regression and correlation analysis for the data on income(Y), the

dependent variable, and credit balance (X), the independent variable, by answering the following.

1.Generate a scatterplot for income ($1,000) versus credit balance($), including the graph of

the best fit line. Interpret.

2.Determine the equation of the best fit line, which describes the relationship between

income and credit balance.

3.Determine the coefficient of correlation. Interpret.

4.Determine the coefficient of determination. Interpret.

5.Test the utility of this regression model (use a two tail test with =.05). Interpret your

results, including the p-value.

6.Based on your findings in 15, what is your opinion about using credit balance to predict

income? Explain.

7.Compute the 95% confidence interval for beta-1 (the population slope). Interpret this

interval.

8.Using an interval, estimate the average income for customers that have credit balance of

$4,000. Interpret this interval.

9.Using an interval, predict the income for a customer that has a credit balance of $4,000.

Interpret this interval.

10.What can we say about the income for a customer that has a credit balance of $10,000?

Explain your answer.

In an attempt to improve the model, we attempt to do a multiple regression model predicting

income based on credit balance, years, and size.

11.Using MINITAB, run the multiple regression analysis using the variables credit balance,

years, and size to predict income. State the equation for this multiple regression model.

12.Perform the global test foruUtility (F-Test). Explain your conclusion.

13.Perform the t-test on each independent variable. Explain your conclusions and clearly

state how you should proceed. In particular, state which independent variables should we keep

and which should be discarded.

14.Is this multiple regression model better than the linear model that we generated in parts

110? Explain.

All DeVry University policies are in effect, including the plagiarism policy.

15. Project Part C report is due by the end of Week 7.

16. Project Part C is worth 100 total points. See the grading rubric below.

Summarize your results from 114 in a report that is 3 pages or less in length and explains and

interprets the results in ways that are understandable to someone who does not know statistics.

Submission: The summary report + all of the work done in 114 (Minitab Output + interpretations)

as an appendix

Format:

A. Summary Report

B. Points 114 addressed with appropriate output, graphs, and interpretations. Be sure to

number each point 114.

Project Part C: Grading Rubric

Category

Questions 112

and 14

5 points each

Points %

Description

65

65

addressed with appropriate output, graphs, and

interpretations

Question 13

15

15

Summary

20

Total

100

addressed with appropriate output, graphs, and

interpretations

20 writing, grammar, clarity, logic, and cohesiveness

A quality paper will meet or exceed all of the

100

above requirements.

**MATH533 DeVry University - Course Project AJ DAVIS - Complete Solution**

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- Submitted On 19 Jan, 2015 09:15:40

**HomeworkExp****Rating :**24**Grade :****A+****Questions :**0**Solutions :**287**Blog :**1**Earned :**$9803.30