10.76 Gender and belief in afterlife The table shows results from the 2014 General Social Survey on gender and whether one believes in an afterlife.

Belief in Afterlife Gender Yes No Total Female 1026 207 1233 Male 757 252 1009

a. Denote the population proportion who believe in an afterlife by p1 for females and by p2 for males.

Estimate p1, p2, and 1p1 - p22.

b. Find the standard error for the estimate of 1p1 - p22.

Interpret.

c. Construct a 95% confidence interval for 1p1 - p22.

Can you conclude which of p1 and p2 is larger? Explain.

d. Suppose that, unknown to us, p1 = 0.81 and p2 = 0.72. Does the confidence interval in part c contain the parameter it is designed to estimate? Explain.