Based on historical data, salespeople at a large consumer goods company are believed to meet on average 15 clients per week, with a standard deviation of 7. To gauge performance by the current cohort of salespeople, a new CEO surveyed 100 randomly-selected employees and found that the sample salespeople met on average 13.5 clients per week. Assume that the historical standard deviation has not changed when this sample was taken. Using = .05, address the following questions: a) Given your sample result, test whether the true mean differs from 15 clients per week. b) Now assume that the true mean is in fact 13 clients per week. If the same hypothesis test is applied as in part (a), what is the probability of committing a type II error ()? c) Now suppose the manager wants to figure out the minimum sample size necessary, such that there is a .9 probability that the sample mean differs from the population mean by at most 1 client (ie, margin of error is 1). How large a sample should he draw? Assume the same population deviation as above. d) Construct a 90 percent confidence interval for the mean number of clients met by salespeople