9.27 In contract negotiations a company claims that a new incentive scheme has resulted in average weekly earnings of at least $400 for all customer service workers.

A union representative takes a random sample of 15 workers and finds that their weekly earnings have an average of $381.35 and a standard deviation of $48.60. Assume a normal distribution.

a. Test the company’s claim.

b. If the same sample results had been obtained from a random sample of 50 employees, could the company’s claim be rejected at a lower significance level than that used in part a?