A U.S. Navy recruiting center knows from past experience that the heights of its recruits have traditionally been normally distributed with mean 69 inches. The recruiting center wants to test the claim that the average height of this year’s recruits is greater than 69 inches. To do this, recruiting personnel take a random sample of 64 recruits from this year and record their heights. The data are provided in the file P09_04.xlsx.
a. Identify the null and alternative hypotheses for this situation.
b. On the basis of the available sample information, do the recruiters find support for the given claim at the 5% significance level? Explain.
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?