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# Distribution Analysis: Statistics for Business Textbook Problems

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6.8 For each of the following rejection regions, sketch the sampling distribution for z and indicate the location of the rejection region.
a. z>1.96
b. z>1.645
c. z>2.575
d. z<-1.28
e. z<-1.645 or z>1.645
f. z<-2575 or z>2.575
g. For each of the rejection regions specified in parts a-f, what is the probability that a Type I error will be made?

6.10 Play Golf America Program. The Professional Golf Association (PGA) and Golf Digest have developed the Play Golf America program, in which teaching professionals at participating golf clubs provide a free 10-minute lesson to new customers. According to Golf Digest (July 2008), golf facilities that participate in the program gain, on average, \$2,400 in green fees, lessons, or equipment expenditures. A teaching professional at a golf club believes that the average gain in greens fees, lessons, or equipment expenditures for participating golf facilities exceeds \$2,400.
a. In order to support the claim made by the teaching professional, what null and alternative hypotheses should you test?
b. Suppose you select alpha = 0.05. Interpret this value in the words of the problem.
c. For alpha = 0.05, specify the rejection region of a large sample test.

6.20 A random sample of 100 observations from a population with standard deviation 60 yielded a sample mean of 110.
a. Test the null hypothesis that u = 100 against the alternative hypothesis that u > 100 using alpha = 0.05. Interpret the results of the test.
b. Test the null hypothesis that u = 100 against the alternative hypothesis that u =/ 100 using alpha = 0.05. Interpret the results of the test.
c. Compare the results of the two tests you conducted. Explain why the results differ.

6.22 Accounting and Machiavellianism. Refer to the Behavioral Research in Accounting (Jan. 2008) study of Machiavellian traits in accountants, Exercise 5.17 (p. 279). A Mach rating score was determined for each in a random sample of 122 purchasing managers with the following results: x-bar = 996, s = 12.6. Recall that a director of purchasing at a major firm claims that the true mean Mach rating score of all purchasing managers is 85.
a. Suppose ou want to test the director's claim. Specify the null and alternative hypothesis for the test.
b. Give the rejection region for the test using alpha = 0.10.
c. Find the value of the test statistic.
d. Use the result, part c, to make the appropriate conclusion.