Descriptive Statistics: [Marks: 7] Based on Mini Case 4.4 from the text book: Numerical studies are helpful when making comparisons (e.g., over time). In Table 5, using data published by the M.P. Power and Associates' (fictitious) Initial Quality Study (ISQ) data, various descriptive measures on number of defects per 100 vehicles are provided for the years 2011 - 2020. Table 5. Measure 2011 2012 2013 2014 2015 2016 2017 2018 2019 2020 Count 50 50 50 50 50 50 50 50 50 50 Sum 3972.00 3960.00 3564.00 3389.00 3269.00 3240.00 3085.00 2702.00 2492.00 2548.00 Mean 79.44 79.20 71.28 57.78 65.38 64.80 61.70 54.04 49.84 50.96 Median 80.00 79.00 71.00 68.00 65.00 64.00 63.00 53.50 50.00 51.00 Standard Deviation 5.70 4.25 4.11 4.21 3.20 5.61 6.90 6.58 6.73 6.10 Coefficient of Variation 7.18 5.36 5.76 6.21 4.89 8.65 11.18 12.18 13.50 11.97 Minimum 71.00 70.00 65.00 60.00 60.00 56.00 50.00 45.00 40.00 40.00 Maximum 90.00 85.00 79.00 75.00 70.00 75.00 70.00 65.00 60.00 60.00 25th Percentile 75.00 77.00 68.00 64.25 62.25 60.00 55.00 48.00 44.00 47.00 275th Percentile 83.00 83.00 74.75 71.00 68.00 69.00 68.75 60.00 56.50 55.75 Answer the following questions based on the output given in Table 5. a) Which year's data has the highest variability? Justify. [1] - 2017 b) For the year 2020, 75th percentile is 55.75. Explain this number. [2] c) Can you comment on shape of the distribution of the data for the year 2014? Please justify. [2] d) Coefficient of variation (CV) is 7.18% for the year 2011. Interpret this value. Why is this measure used? [1] e) What can you say about the general trend of the number of defects per 100 vehicles over the years? [1] 2022[Marks:10] Testing of Hypothesis: From a survey done 2 years back, it was found that the average starting salary for an MBA graduate from one of the top tier business schools in India is Rs. 20 Lakhs per annum. In order to study if there has been a significant increase in the average starting salary per annum for MBA graduates from the same business school, a sample of 28 recent graduates has been considered, and asked about their starting salaries per annum. An appropriate test of hypothesis is performed and the results are provided in Table 4. Assuming that starting salaries per annum follow normal distribution, answer the following questions: Table 4. t-Test: Two-Sample Assuming Unequal Variances Variable 1 Variable 2 Mean 20.0075 0 Variance 0.516686111 0 Observations 28 28 Hypothesized Mean Difference 20 df 27 t Stat 0.055211162 P(T