Use the following information for Exercises 16.10 to 16.12. The distribution of blood cholesterol level in the population of young men aged 20 to 34 years is close to Normal, with standard deviation o = 41 milligrams per deciliter (mg/dl). We measure the blood cholesterol of a random sample of 14 male cross- country runners and find that they have a mean cholesterol level of 172 mg/dl. Assume that o is the same in this population as in the general population of young adult males. 16.10 Blood cholesterol: estimation. Give a 90% confidence interval for the mean cholesterol level µë among male cross-country runners based on our sample. 16.11 Blood cholesterol: testing. The mean blood cholesterol level for all men aged 20 to 34 years is considered to be µ=188 mg/dl.µ = 188 mg/dl. We suspect that the mean for male cross- country runners is lower. a. State the hypotheses. Then find the test statistic and give the P-value based on our sample. Is the result significant at the a=0.10a = 0.10 level? At a=0.05?a = 0.05? At a=0.01?a = 0.01? b. Explain how you can use the confidence interval you computed in Exercise 16.10 to test these hypotheses. What significance level does that 90% confidence interval yield when testing the hypotheses you stated in part a? Remember that your test was one-sided. 16.12 Blood cholesterol: inference conditions. Male cross-country runners as a group are probably more fit than young adult males as a whole, so they may also be more similar to each other physiologically. The inference procedures you used for Exercises 16.10 and 16.11 rely on a number of assumptions. Which of these assumptions may not be reasonable in this specific context? Explain your reasoning.

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