SOLUTION: Suppose that an insurance agent for Almost Heaven Insurance claims that less than 20% of his life insurance policies ever have to "pay out." You decide to test his claim at the a=0

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Question 460948: Suppose that an insurance agent for Almost Heaven Insurance claims that less than 20% of his life insurance policies ever have to "pay out." You decide to test his claim at the a=0.02 significance level. A sample of 75 policies from last year finds that 30 of them had to pay out. The hypotheses is as follows: Ho: p>(underlined) 0.20 and H1: p< 0.20. with a critical value of -2.05 compute the sample statistic and choose the appropriate solution.

Solution is either A) We cannot reject HO, thus it may be that at least 20% of the policies pay out or B) We reject Ho, thus less than 20% of the policies pay out.
Answer by edjones(8007) About Me  (Show Source):
You can put this solution on YOUR website!
H[o]:p<.2 NOT what you have above. He claims that LESS than 20% of his life insurance policies ever have to "pay out." The null hypothesis should be what HE claims.
p[o]=.20, q[o]=.80,
n=75, P=30/75 = .4
s=sqrt(.2*.8*75)=sqrt(12)=3.46
m=.2*75=15
.

=.2/.0462
=4.33
The critical value should be 2.05 NOT -2.05
4.33 is way above 2.05 and the null hypothesis is rejected.
.
Ed