One measure of the quality of education provided by a university is the number of students per class. The president of a large university would like to estimate the true mean size of all thirdyear classes at the university. A random sample of 3G thirdyear dasses is selected. The number of students in each of the classes are ordered and shown below 10,1114, 14,15, 1?,18, 20', 22. 22 22, 23, 2E, 26, 2?, 23, 3'1, 33, 34, 34 36, 42, 44, 43', 5D, 55, 62, 25, 7'7, 82 The mean and standard deviation of these 3G observations is calculated to be 33.9? and 19.91, respectively. Based on the provided information, oonduct an appropriate hypothesis test at the 5% level of signicance to determine whether there is evidence that the true mean thirdyear class size at this university is greater than the national average of 44. Provide the following: [a] What are the null and alternative hypothesis? ['1 mark} [b] test statistic value, please also indicate type of test being used [2 or t] {2 marks} {c} Pvalue [1 mark] [cl] oonclusion {1 mark} {e} if we consthct a 93% condence interval to estimate the true mean of the population, what would be the margin of errors. {'1 mark}