Brand managers become concerned if they discover that customers are aging and moving out of the high-spending age groups. For example, the average Cadillac buyer is older than 60, past the prime middle years that typically are 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 customers. If a sample of 50 Escalade purchasers has an average age of 45 with a standard deviation of 25, is this compelling evidence that Escalade buyers are younger on average than the typical Cadillac buyer?

1. What are the null and alternative hypotheses here?
2. What would the Type I and Type II errors mean here?
3. Calculate the test statistic for this sample result.
4. What is your conclusion (use a = 0.01)?