# Solve: Hypothesis Testing and Regression Analysis

The null and alternate hypotheses are:

H0: U1 = U2

H1: U1 does not = U2

A random sample of 15 observations from the first population revealed a sample mean of 350 and a sample standard deviation of 12. A random sample of 17 observations from the second population revealed a sample mean of 342 and a sample standard deviation of 15. At the .10 significance level, is there a difference in the population means?

1. Ms. Lisa Monnin is the budget director for Nexus Media, Inc. She would like to compare the daily travel expenses for the sales staff and the audit staff. She collected the following sample information.

Sales ($) 131 135 146 165 136 142

Audit ($) 130 102 129 143 149 120 139

At the .10 significance level, can she conclude that the mean daily expenses are greater for the sales staff than the audit staff? What is the p-value?

2. The management of Discount Furniture, a chain of discount furniture stores in the Northeast, designed an incentive plan for salespeople. To evaluate this innovative plan, 12 salespeople were selected at random, and their weekly incomes before and after the plan were recorded.

Salesperson............................Before............After

Sid Mahone .............................$320.............$340

Carol Quick..............................290...............285

Tom Jackson............................421...............475

Andy Jones..............................510...............510

Jean Sloan...............................210...............210

Jack Walker.............................402...............500

Peg Mancuso...........................625...............631

Anita Loma..............................560................560

John Cuso...............................360...............365

Carl Utz....................................431..............431

A. S. Kushner..........................506...............525

Fern Lawton............................505..............619

Was there a significant increase in the typical salesperson's weekly income due to the innovative incentive plan? Use the .05 significance level. Estimate the p-value, and interpret it.

3. Fairfield Homes is developing two parcels near Pigeon Fork, Tennessee. In order to test different advertising approaches, they use different media to reach potential buyers. The mean annual family income for 75 people making inquiries at the first development is $150,000, with a standard deviation of $40,000. A corresponding sample of 120 people at the second development had a mean of $180,000, with a standard deviation of $30,000. At the .05 significance level, can Fairfield conclude that the population means are different.

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#### Solution Summary

This solution gives details of a student's t test and regression analysis. This discussion includes the concepts of the null hypothesis, alternative hypothesis, critical value, p value, regression, slope, intercept, correlation, r square value, coefficient of determination, regression coefficients, least square estimation and a scatter diagram. An interpretation of the results is also presented with the solution which is enclosed within an attached Word document.