# Math Help - hypothesis test

1. ## hypothesis test

Suppose that n measurements are to be taken under a treatment condition and another n measurements are to be taken independently under a control condition. it is thought that the Standard deviation of a single observation is about 10 under both conditions. how large n should be so that the test of H0: mu_x=mu_y against the one sided alternative Ha: mu_x > mu_y has a power of 0.5 if mu_x-mu_y=2 and significant level = 0.1

Thanks!

2. The formula is

$n\ge {(z_{\alpha}+z_{\beta})^2\sigma^2\over \delta^2}$

Actually that's a one sample case.
I might have to derive the two sample case, since the st deviation is different.

It's on the next page of walpole...

$n\ge {(z_{\alpha}+z_{\beta})^2(\sigma_1^2+\sigma_2^2)\o ver \delta^2}$

But that was derived for a two-sided test.
I may have to think about it.