# Question: how do you find rejection regions heres the question two...

###### Question details

How do you find rejection regions?

Here's the question:

Two different companies have applied to provide cable television service in a certain region. Let p denote the proportion of all potential subscribers who favor the first company over the second. Consider testing H_0: p =0.5 vs. H_a: p != 0.5 based on a random sample of 25. Let the test statistic X be the number in the sample who favor the first company and x represent the observed value of X.

d) if H_0 is to be rejected when the p-value <= .044, compute the probability of a type II error when p = .4, again when p = .3, and also when p = .6 and p = .7 (hint: p-value >.044 is equivalent to what inequalities involving x?)

So how do you find the rejection region for this problem? Then how do you solve for each p? Please show all steps.