A poll conducted by Gallup asked American adults about vegetarianism. This problem is based on that poll. Of independent random samples of 500 men and 512 women, 20 of the men and 36 of the women said they were vegetarians. At the 5% significance level do the data provide sufficient evidence to conclude that a difference exists in the proportions of male and female vegetarians?
a. Use the two-proportions z-test (Procedure 12.3 on page 564) to perform the required hypothesis test.
b. Use the chi-square homogeneity test to perform the required hypothesis test.
c. Compare your results in parts (a) and (b).
d. Explain what principle is being illustrated.