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Question 1 (14 marks) Call centers play an important role in managing day-to-day business communications with customers. It is of vital importance to monitor a comprehensive set of service quality dimensions, which can help businesses understand the overall performance of a call center. One key dimension for measuring overall call center performance is service time which is defined as the time to answer an incoming call. Assume that the service time is independent and has a normal distribution. The data for time, in seconds, to answer randomly selected 36 incoming calls to a financial services call center are 16 14 16 19 6 14 15 5 16 18 17 22 6 18 10 15 12 6 19 16 16 15 13 25 9 17 12 10 5 15 23 11 12 14 24 12 (a) Find the sample mean and sample variance of the service times. (2 marks) (b) At 0.05 level of significance, conduct a hypothesis test for whether there is evidence that the mean service time is less than 16 seconds? (9 marks) (c) Among the 36 incoming calls, 11 are answered by Alan, 12 by Betty and 13 by Calvin. Their supervisor is going to review exactly one call by each of them. Find the total number of possible combinations in the review