Let X1, middot middot middot , Xn be iid Np( mu , ), where both mu and are unkno

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Let X1, middot middot middot , Xn be iid Np( mu , ), where both mu and are unknown. For I = 1, middot middot middot, n, let be the ith vector of sample P.C.'s, corresponding to the ith observation Xi. (Thus, for example, see the notes for the notation.) Consider testing H0 : mu = 0 versus at significance level a1 based on Hotelling's T2 statistic: T2(X1, middot middot middot , Xn) = Now suppose that, by mistake, one is using the statistic T2 instead of T2(X1, middot middot middot , Xn). How would this mistake change the rejection region of the test? Clearly show your work and derivations.

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Let X1, middot middot middot , Xn be iid Np( mu , ), where both mu and are unkno

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