In 1960, census results indicated that the age at which men in a certain region first married had a mean of 24.5 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 from 24.5 years since then. A) Write appropriate hypotheses
B) The 40 men in our sample first married at an average age of 25.4 years, with a sample standard deviation s of 5.3 years. Calculate the test statistic t. What's the P-value for this result?
C) Describe the approximate sampling distribution model for the mean age in such samples.
D) 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.
E) Explain (in context) what this P-value means.
F) What's your conclusion?