# Thread: hypothesis testing

1. ## hypothesis testing

Suppose Y ~ N(mu, 225) and X represents the mean of a sample size of n=25. We wish to test the null hypothesis mu =60 with the greater than composite alternative using the rejection region {x l x > 63.8}.
A) Comput alpha(level of significance)
B) if the true value of mu = 64 compute beta

Thanks for the help

2. $\alpha = P(\bar X>63.8)=P\biggl(Z>{63.8-60\over 15/\sqrt{25}}\biggr)\approx P(Z>1.27)$.

Now $\beta$ is the opposite, BUT now the mean is 64.

$\beta = P(\bar X\le 63.8)=P\biggl(Z\le {63.8-64\over 15/\sqrt{25}}\biggr)$....