Question

7. A scientist has a theory that more than 33% of geese in his area do not fly south for the winter. To test this hypothesis he tags 85 random geese in the summer and finds that 40% of them do not fly south. Test the hypothesis using a = .05. (A) Do not reject Ho, because the test value of 1.37 is less than 1.96. (B) Do not reject Ho, because the p-value is equal to .4147 which is greater than 05. (C) Do not reject Ho, because the test value of 1.32 is less than 1.645. (D) Do not reject Ho, because the p-value is equal to .1706 which is greater than .05. (E) Do not reject Ho, because the test value of 1.37 is less than 1.645.

Why is the answer 1.37 and not 1.32. I did this myself:

Answer 1

Below are the null and alternative Hypothesis,
Null Hypothesis: p = 0.33
Alternative Hypothesis: p > 0.33

Rejection Region
This is right tailed test, for α = 0.05
Critical value of z is 1.645.
Hence reject H0 if z > 1.645

Test statistic,
z = (pcap - p)/sqrt(p*(1-p)/n)
z = (0.4 - 0.33)/sqrt(0.33*(1-0.33)/85)
z = 1.37

Hence Option E is correct.