The proportion of adults living in a small town who are college graduates is estimated to be p = 0.6. To test this hypothesis, a random sample of 15 adults is selected. If the number of college graduates in the sample is anywhere from 6 to 12, we shall not reject the null hypothesis that p = 0.6; otherwise, we shall conclude that p /= 0.6.

Question

The proportion of adults living in a small town who are college graduates is estimated to be p = 0.6. To test this hypothesis, a random sample of 15 adults is selected. If the number of college graduates in the sample is anywhere from 6 to 12, we shall not reject the null hypothesis that p = 0.6; otherwise, we shall conclude that p /= 0.6.

Evaluate β for the alternatives p = 0.5 and p = 0.7.

Beta is The probability of Type 2 error. 
I tried to use the binomial distribution with n=15 and p=.5 and .7 to get P(6<=x<=12|p=.5) and use 12 and 6 for x and substract the results but I can't get the correct answers which are 0.8454 for p=0.5, and 0.8695 for p=0.7 
Is there another way of doing it? Are my x's right for the binomial distribution right?

Kuai · Answer

β = P(Type II Error) =P(6≤X ≤13|p=0.5) (0.5)^x(0.5)^15-x ≈ 0.8454 β = P(Type II Error) =P(6≤X ≤13|p=0.7 0.7^x (0.3)^15-x ≈

Kuai · Answer

you're right