Thread: Coin Flip Hypothesis Testing

So I glanced at the overall Hypothesis Testing thread and other articles on the internet and it seems most of them cover standard deviations and other stuff that we haven't quite got to yet in class. Me and my friend were reviewing the home work and we keep getting confused with the hypothesis testing.

Problem:
Consider the coin flip example from class. Our hypotheses were H0: PI = 0.5 vs.
Ha:  PI> 0:5. Compute the probability of a type II error at PI  = 0.7 when we reject
H0 if the coin comes up heads every time after

(a) n = 1 flip

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A type II error is accept the null (coin is fair with a .5 probability) even though it is unfair with a .7 probability. Would the probability of this simply be 1-(0.7)^n with n being the number of flips or am I way off base?

What is your critical region and what is PI?