Question: Consider a single sample case, where we wish to make a test on the mean () of a normal population, with unknown variance. We ask,

Consider a single sample case, where we wish to make a test on the mean () of a normal population, with unknown variance. We ask, is it zero? From Section 5.2, the point-null hypothesis Ho postulates that =o = 0. From Tables 5.4 and 5.7 we reject this hypothesis if |T|> t- where T = Show that this decision procedure is the same as finding that the a-level two-sided confidence interval for does not include zero. Se 5.4 Show that the one-to-one correspondence considered in Problem 5.3 also holds for one-sided confidence interval and one-sided tests on single samples.

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