Table 7.14 summarizes responses from General Social Surveys in 1977 and in 2014 to the statement “It is much better for everyone involved if the man is the achiever outside the home and the woman takes care of the home and family.” Let π1 denote the population proportion who agreed with this statement in 1977, and let π2 denote the population proportion in 2014.

(a) Show that πˆ 1 − πˆ 2 = 0.347, with standard error 0.017.

(b) Show that the 95% confidence interval for π1 − π2 is (0.31, 0.38). Interpret.

(c) Explain how results would differ for comparing the proportions who did not agree in the two years.