5. In 1960, census results indicated that the age at which American men rst married had a mean of 23.3 years. It is widely suspected that young people today are waiting longer to get married. We want to find out if the mean age of first marriage has increased during the past 43 years. arcs Write out the appropriate hypotheses. We plan to test our hypothesis by selecting a random sample of 64 men who married for the rst time last year. Do you think the necessary assumptions for inference (such as for testing of hypothesis and for constructing condence interval) are satised? Explain. Write down the approximate sampling distribution of the sample statistic f in your answer sheet by replacing the symbols below by numbers that you know from the information given. 3 ~ Normau, GAG) The men in our sample married at an average age of 24.2 years with a standard deviation of 5.3 years. Carry out an appropriate test at 1% signicance level, using the critical value approach. That is, find the appropriate critical region, make decision and write your conclusion. Find the pvalue for the test and make sure that your acceptance-rejection decision remains the same if the p-value approach is adopted. Explain in your own words and as explained in class, how you interpret this p-value. Without doing any calculations, explain what would happen if i} Ha: p = 27.0. Would the power increase or decrease against this new alternative? Explain. ii) Old alternative remains, but sample size is increased. lMould the power increase or decrease? Explain. Find a 99% condence interval for the for the unknown population average age at marriage. Explain in your own words and as explained in class what you mean by this confidence interval. Now write a two-tailed test with the appropriate null and alternative hypotheses for problem in (a) through (d). Is 23.3 included in the 99% condence interval you created in (a) above? Whatever may be the case, explain the implications clearly