Linear Plexing

We have fixed $\alpha$ as the maximum acceptable probability of commiting atype $I$ error. But associated with each normalized test of significance is$\gamma$, the probability of commiting a type $I$ error.

Notice that as we make $\gamma$ smaller, the smaller the critical regionbecomes and thus the larger the value of the test statistic must be for thenull hypothesis to be rejected.

Find $p$, defined as the smallest $\gamma$ for which we can still reject$H_0$.

Reject $H_0$ if .