A market researcher for an automobile manufacturer intends to conduct a nationwide survey concerning car repairs. Among the questions included in the survey is the following: "What was the cost of all repairs performed on your car last year?" In order to determine the sample size necessary, the researcher needs to provide an estimate of the standard deviation. Using his past experience and judgment, he estimates that the standard deviation of the amount of repairs is $200. Suppose that a small-scale study of 25 auto owners selected at random indicates a sample standard deviation of $237.52.
a. At the 0.05 level of significance, is there evidence that the population standard deviation is different from $200?
b. What assumption do you need to make in order to perform this test?
c. Compute the p-value in part (a) and interpret its meaning.