A 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 severalyears, the lengths of telephone calls(in minutes) were normally distributed with =15 and =6. The service arranged to have the special phone system loaned to them for one day. On thatday, the mean length of the 45 calls they received was 18 minutes. Test whether the length of calls has changed using the5% significance level. Complete parts(a) through(d)

PS: for The part C: (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.

The distribution of means uses many samples of (the same size, different size) with each sample randomly taken from the population of individuals. Since the sample score could occur by chance (5% of the time or less/more than 5% of the time)

the results (support/do not support) the hypothesis that the length of calls is affected by better call sound quality. In thissituation, the researcher is finding a Z score of thesample's mean on a distribution of means instead of finding the Z score of a single individual on a distribution of single individuals. The sample mean is being treated as (a single score/45 scores)