Question: Here is another common interpretation of p-values. Consider a problem of testing H0 versus H1. Let W(X) be a test statistic. Suppose that for each

Here is another common interpretation of p-values. Consider a problem of testing H0 versus H1. Let W(X) be a test statistic. Suppose that for each a, 0 ≤ a ≤ 1, a critical value ca can be chosen so that {x : W(x) ≥ ca} is the rejection region of a size a test of H0- Using this family of tests, show that the usual p-value p(x), defined by (8.3.9), is the smallest α level at which we could reject H0, having observed the data x.

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