The marketing manager of a branch office of a local telephone operating company wants to study characteristics of residential customers served by her office. In particular, she wants to estimate the mean monthly cost of calls within the local calling region. In order to determine the sample size necessary, she needs an estimate of the standard deviation. On the basis of her past experience and judgment, she estimates that the standard deviation is equal to $12. Suppose that a small-scale study of 15 residential customers indicates a sample standard deviation of $9.25.
a. At the 0.10 level of significance, is there evidence that the population standard deviation is different from $12?
b. What assumption do you need to make in order to perform this test?
c. Compute the p-value in (a) and interpret its meaning.