21. [20 Marks]. Suppose a reviewer took a random sample of 20 days' worth of lectures and gave them a score out of 50 for their quality. This sample is given Day Score 5 23 3 7 4 17 9 15 24 17 11 10 10 11 4 16 13 23 14 14 15 19 16 40 17 13 18 35 19 9 20 18 a. Use the Excel's Descriptive Statistics Functions under "Data Analysis" to obtain a range of statistics that can be used to describe the range of quality scores. Then, calculate a 90% confidence interval for the true population mean of the quality score. Paste your output below.b. Provide a point estimate for the mean quality score for the lectures. C. Interpret the sample standard deviation (i.e. 's") in context. d. Draw a histogram to show the frequency of transactions with different quality scores; use "buckets" of 5 (e.g. 0-4, 5-9 etc) e. Provide and interpret a 90% confidence interval for the mean. The reviewer needs to recommend a wider investigation into lecture quality if the quality score is below 10, should the reviewer recommend this course of action. f.A policy change means the reviewer now needs to recommend a wider investigation into lecture quality if the quality score is below 15. Using a hypothesis test based on the test statistic or p- value approach, should the reviewer recommend a wider investigation. State your null and alternative hypothesis and conclusion (and how you got to it) clearly. Work at 95% confidence