When the population distribution is normal and n is large,the sample standard deviation

Chapter 8, Problem 84

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When the population distribution is normal and n is large,the sample standard deviation S has approximately a normaldistribution with and . We alreadyknow that in this case, for any n, is normal withand .a. Assuming that the underlying distribution is normal,what is an approximately unbiased estimator of the 99thpercentile ?b. When the Xis are normal, it can be shown that and Sare independent rvs (one measures location whereas the other measures spread). Use this to compute andfor the estimator of part (a). What is the estimatedstandard error ?c. Write a test statistic for testing that hasapproximately a standard normal distribution when H0 istrue. If soil pH is normally distributed in a certain regionand 64 soil samples yield , does thisprovide strong evidence for concluding that at most 99%of all possible samples would have a pH of less than6.75? Test using .

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