Question

Define α\alpha and β\beta for a statistical test of hypothesis.

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For a statistical hypothesis problem H0H_0 vs HaH_a, the Type-I error\textit{Type-I error} or the level of significance\textit{level of significance} α\alpha of the test is defined as

α=P(Reject H0 when it is true)\alpha = P(\text{Reject $H_0$ when it is true})

For the problem the Type-II error\textit{Type-II error} β\beta is defined as:

β=P(accept h0 when it is false)\beta = P(\text{accept $h_0$ when it is false})

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