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    Solve: Hypothesis Testing and Regression Analysis

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    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.

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