Question: Problem 2. (10 pts.) Height. Suppose / is the average height of a college male. You measure the heights (in inches) of twenty college men,

Problem 2. (10 pts.) Height. Suppose / is the average height of a college male. You measure the heights (in inches) of twenty college men, getting data 1, ..., 120, with sample mean I = 69.55 in. and sample variance $2 = 14.26 in'. Suppose that the r; are drawn from a normal distribution with unknown mean / and unknown variance o. (a) Using I and s', construct a 90% t confidence interval for p. (b) Now suppose you are told that the height of a college male is normally distributed with standard deviation 3.77 in. Construct a 90% z confidence interval for /. (c) In (b), how many people in total would you need to measure to bring the width of the 90% z confidence interval down to 1 inch? (d) Consider again the case of unknown variance in (a). Based on this sample variance of 14.26 in , how many people in total should you expect to need to measure to bring the width of the 90% t confidence interval down to 1 inch? Is it guaranteed that this number will be sufficient? Explain your reasoning

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