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In 1960, census results indicated that the age at which men in a certain region first married had a mean of 23.1 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 since then. Complete parts a through f below. a) Write appropriate hypotheses. HA: b) We plan to test our hypothesis by selecting a random sample of 40 men who married for the first time last year. Do you think the necessary assumptions for inference are satisfied? Explain. The independence condition satisfied and the Nearly Normal Condition satisfied because Therefore, using the Student-t model for inference reliable. c) Describe the approximate sampling distribution model for the test statistic. Select the correct choice below and fill in the answer boxes to complete your choice. (Type exact answers, using radicals as needed.) y - HO O A. The test statistic has the form t = - SE (y) , where Ho = and SE (y) = s. This follows a t distribution with degrees of freedom. y - HO O B. The test statistic has the form t = , where Ho = and SE (y) = . This follows a normal distribution. SE (y) y - HO O C. The test statistic has the form t = - SE (y) , where Ho = and SE (y) = . This follows a t distribution with degrees of freedom. d) The men in our sample married at an average age of 24.1 years, with a standard deviation of 5.4 years. That results in a t-statistic of 1.171. What is the P-value for this? The P-value is. (Round to three decimal places as needed.) e) Explain (in context) what this P-value means. The P-value is the probability from natural sampling variation given that f) What is your conclusion? Use a = 0.05. the null hypothesis. There | sufficient evidence to conclude that the mean age of first marriage is the mean age in 1960