a 8. (24 points) Significance Test A student uses pens whose lifetime X is an exponential random variable with mean of 1

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A 8 24 Points Significance Test A Student Uses Pens Whose Lifetime X Is An Exponential Random Variable With Mean Of 1 1 (198.35 KiB) Viewed 33 times

a 8. (24 points) Significance Test A student uses pens whose lifetime X is an exponential random variable with mean of 1 week. a) (12 pts) Use the central limit theorem to determine the minimum number of pens he should buy at the beginning of a 16-week semester, so that with probability 0.99 he does not run out of pens during the semester, i.e., determine the smallest value of n, such that P[Sn > 16) > 0.99, where Sn = 21=1 Xị. b) (12 pts) The student uses the sample mean of the lifetime of n pens (please use the n found in part a)) as a statistic in a significance test for the null hypothesis (Ho: the average pen lifetime is 1 week). Find a test at a 1% significance level, that is, find a rejection region Ř that P[in E H.] = 0.05. a =