### 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 $3200.

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.

Follow this up with computing 95% confidence intervals for each of the variables described in a.-d., and again interpreting these intervals.

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.

**Project Part C: Regression and Correlation Analysis**

Using MINITAB perform the regression and correlation analysis for the data on CREDIT BALANCE (Y) and SIZE (X) by answering the following.

1. Generate a scatterplot for INCOME ($1000) vs. CREDIT BALANCE($), 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.

11. In an attempt to improve the model, we attempt to do a multiple regression model predicting INCOME based on CREDIT BALANCE, YEARS and SIZE.

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 for Utility (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, 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.

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