21. A government-sponsored telephone counseling service for adolescents tested whether the length of calls would be affected by a special telephone system that had a better sound quality. Over the past several years, the lengths of telephone calls (in minutes) were normally distributed with  = 18 and  = 8. They arranged to have the special phone system loaned to them for one day. On that day, the mean length of the 46 calls they received was 21 minutes. Test whether the length of calls has changed using the 5% significance level.

(a) Carry out a Z test using the five steps of hypothesis testing.

(b) Make a drawing of the distributions involved.

(c) Explain your answer to someone who knows about hypothesis testing with a sample of a single individual but who knows nothing about hypothesis testing with samples of more than one individual.

(d) ADVANCED TOPIC: Figure the 95% confidence interval.