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Hypothesis Testing of Means

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The Non-Profit Times conducted a random sample of 126 U.S. non-profit companies at the beginning of 2005. The results reported that the average salary of an executive director of a nonprofit was $92,411 per year with a sample standard deviation of $25,326. A research team from a competing newspaper, which was skeptical of these results, conducted a survey of its own with the same size sample of companies and obtained a mean salary of $87,566 for executive directors (with approx. the same standard deviation as the non-profit times sample).

1)Set up the appropriate null and alternative hypothesis for testing whether the original sample overestimated the average executive director annual salary.

2)Now test the competing newspaper's view that the original sample overestimated the average executive director annual salary. Use an estimation (total) error of 5 percent.

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Solution:

1.)Set up the appropriate null and alternative hypothesis for testing whether the original sample overestimated the average executive director annual salary.
Ho: There is not difference in salary
H1: original newspaper overestimated average executive's ...

Solution Summary

Solution describes Null and Alternate hypothesis for testing whether the original sample overestimated the average executive director annual salary. It also tests the competing newspaper's view that the original sample overestimated the average executive director annual salary

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Franklin Park Mall Hypothesis Testing

The owners of the Franklin Park Mall wished to study customer shopping habits. From earlier
studies the owners are under the impression that a typical shopper spends 0.75 hours at the mall,
with a standard deviation of 0.10 hours. Recently the mall owners added some specialty restaurants designed to keep shoppers in the mall longer. The consulting firm, Brunner and Swanson Marketing Enterprises, has been hired to evaluate the effects of the restaurants. A sample of 45 shoppers by Brunner and Swanson revealed that the mean time spent in the mall had increased to 0.80 hours.
a. Develop a test of hypothesis to determine if the mean time spent in the mall is more than
0.75 hours. Use the .05 significance level.
b. Suppose the mean shopping time actually increased from 0.75 hours to 0.77 hours. What is
the probability this increase would not be detected?
c. When Brunner and Swanson reported the information in part (b) to the mall owners, the owners
were upset with the statement that a survey could not detect a change from 0.75 to 0.77
hours of shopping time. How could this probability be reduced?

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