The following table summarizes responses from GSS in 1977 and 2006 to the question, "It is much better for everyone involved if the man is the achiever outside the family and the woman takes care of the home and family." Let 71 denote the population proportion who agreed with this statement in 1977, and let 72 denote the population proportion who agreed with this statement in 2006. a. Find a 95% confidence interval for the difference in the two proportions. b. Is there significant evidence (at the level of 5% ) that the two proportions differ? State the null and alternate hypotheses, and report the value of the test statistic and the critical value used to conduct the test. Report your decision regarding the null hypothesis and your conclusion in the context of the problem. Year Agree Disagree Total 1977 989 514 1503 2006 704 1264 1968