Computing sample size and Best Critical Region

[Cynderella]

Let \(X_1,X_2,\ldots,X_n\) denote a random sample from a normal distribution \(N(\theta,100)\).

Show that \(C=[(x_1,x_2,\ldots,x_n):c\leq \bar x=\frac{\sum_1^n x_i}{n}]\)

is a best critical region for testing \(H_o:\theta=75\) against \(H_1:\theta=78\).

Find \(n\) and \(c\) so that

\(P[(X_1,X_2,\ldots,X_n)\epsilon C;H_o]=P(\bar X\geq c;H_o)=0.05\)
and
\(P[(X_1,X_2,\ldots,X_n)\epsilon C;H_1]=P(\bar X\geq c;H_1)=0.90\)

approximately.

 

[Dason]

Hi! :welcome: We are glad that you posted here! This looks like a homework question though. Our homework help policy can be found here. We mainly just want to see what you have tried so far and that you have put some effort into the problem. I would also suggest checking out this thread for some guidelines on smart posting behavior that can help you get answers that are better much more quickly.