Question: Time magazine reported that in a 1994 survey of 507 randomly selected adult American Catholics, 59% answered yes to the question "Do you favor allowing women to be priests?" (Time, 26 December-2 January 1995, pp. 74 -76).
a. Set up the null and alternative hypotheses for deciding whether more than half of American Catholics in 1994 favored allowing women to be priests.
b. What conditions are necessary for using a z-statistic to test the hypotheses in part (a)? Are those conditions met here? Explain.
c. Compute the test statistic for this situation.
d. Calculate the p-value for the test.
e. On the basis of the p-value, make a conclusion for this situation. Use level of significance a = .05. Write the conclusion in both statistical language and in words that someone with no training in statistics would understand.
f. Calculate a two-sided 95% confidence interval for the proportion of American Catholics in 1994 who favored allowing women to be priests. Does the interval support the conclusion that a majority of American Catholics in 1994 favored allowing women priests? Explain.