90. When the population distribution is normal and n is large, the sample standard deviation S has approximately a normal distribution with E(S)  s and V(S)s2/(2n).We already knowthat in this case, for any n, is normal with and

a. Assuming that the underlying distribution is normal, what is an approximately unbiased estimator of the 99th percentile u  m  2.33s?

b. As discussed in Section 6.4, when the Xi s are normal and S are independent rv s (one measures location whereas the other measures spread). Use this to compute and for the estimator of part (a). What is the estimated standard error ?

c. Write a test statistic for testing H0: uu0 that has approximately a standard normal distribution when H0 is true. If soil pH is normally distributed in a certain region and 64 soil samples yield

, s  .16, does this provide strong evidence for concluding that at most 99% of all possible samples would have a pH of less than 6.75?

Test using a  .01.