Proving Power Function for H0: p=1/2 in Coin Bias Test | X=8, 9, or 10

[sara_87]

A coin is suspected of bias towards heads, so a test is made of the hypothesis H0: p=1/2 against H1:p>1/2, where p is the probability of heads. The test is to count the number of heads, X, in 10 tosses of the coin, and reject H0 if X=8, 9, or 10.
Show that the power function for this test is given by: p^8(45-80p+36p^2)

I have no idea how to start. I know that the power function means: P(reject H0 given H0 is false) but i don't know how to continue.

Any help would be very much appreciated.
Thank you

 

[EnumaElish]

I think you can ignore the part "given H0 is false" because the test is expressed for an arbitrary p (which may or may not be the value of p under H1).

So, all you need is to express the probability of obtaining X > 7 in 10 throws using the binomial formula.

 

[sara_87]

Oh right
Thank you v much!
(I should have known that)