The question is as follows:
Let X be a variable with bin(25,p)-distribution. We test $H_{0}$: p $\geq$ 0.4 against $H_{1}$: p < 0.4. If we want a power function of at least 0.6 in p = 0.3, how large must we choose the size of the test at least?
I'm not really sure what the right approach is here. Do I have to compute the critical region first?
I know the critical region is like: {0,...,$c_{\alpha_{0}}$}, and
$P_{0.3}$(X$\leq c_{\alpha_{0}}$) $\geq$ 0.6, to compute this I can use the normal approximation.
Can someone tell me what the approach is? :) Thanks
Out of the four quantities significance level $\alpha,$ power, sample size, and difference $\Delta$ detected, a power computation typically specifies three and finds the remaining one.
The following power curve from Minitab uses $\alpha = 0.05, n = 25, \Delta = .4 -.3 = .1,$ and shows power for a range of 'comparison' values (.3 above).
With $\alpha = 0.05,$ the rejection region is too small to get 0.6 power against $\mu_a = .3.$ So you need larger $\alpha.$ What critical value $c$ gives power 0.6? What $\alpha$ is implied by that?
Maybe this will help you clarify a productive approach to your Question.