Statistics

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's—be 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.

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 manager’s belief in each case A–D. In each case, use the Seven Elements of a Test of Hypothesis in Section 6.2 of your text book with α = .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 A–D, 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.

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:

1. Summary report (about one paragraph on each of the speculations, A–D)
2. 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 A–D, as well as the confidence intervals, including all minitab output 

 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 α =.05). Interpret your results, including the p-value.

6.        Based on your findings in 1–5, 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 1–10? Explain.

Summarize your results from 1–14 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 1–14 (Minitab Output + interpretations) as an appendix

Format:

1. Summary Report
2. Points 1–14 addressed with appropriate output, graphs, and interpretations. Be sure to number each point 1–14.