In 2000, census results indicated that the age at which Hong Kong women first married had a mean of 26.3 years. It is widely suspected that young people today are waiting longer to get married. We want to find out if the mean age at first marriage has increased during the past 20 years. We plan to test our hypothesis by selecting a random sample of 100 women who married for the first time last year. The men in our sample married at an average age of 29.2 years, with a standard deviation of 4.3 years. (a) At a 5% level, test the hypothesis that average age of first marriage has increased in the past 20 years. (b) Give a symmetric 95% confidence interval for the difference in average marriage age between the two populations