Question: 2. Let X1, ..., X10 be a random sample of size 10 from a N(u, 1) distribution. (a) Consider testing Ho : M = MO

2. Let X1, ..., X10 be a random sample of size 10 from a N(u, 1) distribution. (a) Consider testing Ho : M = MO V.S. H1 : M # Mo using the following "confidence interval" approach: we reject Ho if and only if Mo does not belong to the 95% confidence interval [X - 1.96/V10, X + 1.96/V10]. Show that the resulting test has significance level a = 0.05. (b) Now suppose we have observed x1, . .., 10, and have computed the sample mean x = 1.6 out of these numbers. We reject Ho when (x - Mo| > 1.96/V10. Find all the values of No such that we do not reject Ho : M = Mo based on the above rejection rule. Compare the values of Mo you find with the realization of the 95% CI for u on this dataset

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