Question: A U.S. Navy recruiting center knows from past experience that the heights of its recruits are normally distributed with mean 68 inches. The recruiting center wants to test the claim that the average height of this year’s recruits is greater than 68 inches . To do this, recruiting personnel take a random sample of 64 recruits from this year and record their heights (in inches). -- use File 2-2.Xl s .

1. On the basis of the available sample information, do the recruiters find support for the given claim at the 1% significance level? Explain. You must also report the null and the alternative hypotheses of the test. [Note: You have no information on the population standard deviation.] (use T- distribution)

b. For which values of the sample mean (i.e., average height of this year’s recruits) would the recruit center be able to find support for its claim? Assume that α = 0.05 in answering this question.

c. Use the sample data to construct a 95% confidence interval for the average height of this year’s recruits. Based on this confidence interval what conclusion should recruiting personnel reach regarding the given claim ?

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