2 The Academic Planning and Delivery Department (APAD) is concerned about the impact of full-time college students working while they are enrolled in classes, and they would like to know if students work too much and therefore are spending less time on their classes than they should be. First, they need to find out, on average, how many hours per week students are working. They know from previous studies that the standard deviation of this variable is about 10 hours. A survey of 50 full-time Open Campus students provides a sample mean of 20 hours worked per week. a. APAD wants to construct a 99% confidence interval for the mean number of hours worked by college students. Explain to the APAD why a larger sample may give a better interval estimate than a sample of 50. b. To prove your point to APAD, calculate the margin of error for a 99% confidence level using a sample of 50 students and a larger sample of your choice. c. Suppose one day, a member of APAD finds a full-time student who works more than the number of hours per week estimated by the 99% confidence interval calculated from the information in part a. Explain to the APAD how this is possible