Brand managers become concerned if they discover that customers are aging and gradually moving out of the high-spending age groups. For example, the average Cadillac buyer is older than 60, past the prime middle years that are typically associated with more spending. Part of the importance to Cadillac of the success of the Escalade model has been its ability to draw in younger consumers. If a sample of 41 Escalade purchasers has an average age of 50 with a standard deviation of 22, is this compelling evidence that Escalade buyers are younger on average than the typical Cadillac buyer? (Assume that the Central Limit Theorem holds and that alpha = 0.10) (a) State the null and alternative hypotheses.
(b) In the context of this problem, explain when Type I and Type II errors would be committed.
(c) What is the test statistic for this hypothesis test?
(d) What is the relevant critical value for this hypothesis test?
(e) What is your conclusion for this hypothesis test?