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Consider the normal distribution with unknown mean μ and unknown variance σ2, and suppose that it is desired to test the following hypotheses:
H0: μ ≤ μ0,
H1: μ>μ0.
Suppose that it is possible to observe only a single value of X from this distribution, but that an independent random sample of n observations Y1, . . . , Yn is available from the normal distribution with known mean 0 and the same variance σ2 as for X. Show how to carry out a test of the hypotheses H0 and H1 based on the t distribution with n degrees of freedom. |
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