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Problem 9. (12 points) Ownomo, the urgent care clinic. is assessing the effectiveness of its current administrative practices to reduce patient waiting times. Staff at Ownomo collected a sample of IS patient wait times with sample mean 34.8 minutes and sample standard deviation 29.1 minutes. Based on this sample. the staff will estimate the average patient time. You may assume the sample is a simple random sample from the population of the patients' waiting times and contains no outliers. (a) (3 points) Report an appropriate 95% condence interval estimate for population mean of patient wait time visiting Ownomo. Show your work. including any calculator functions you use. (b) (3 points) What was the margin of error of the condence interval constructed in Part (a)? (c) (3 points) If we wanted to be 99% condent that our estimate was within 2 of the population mean of patient wait time. how many patients should we observe? Use the sample standard deviation instead of a in the formula you would use. (d) (3 points) If the sample included more patients. would the 99% condence interval have been narrower or wider than the interval constructed in Part (a)