A random sample of 25 taken from the students taking in 2015 and the second random sample of 16 taken from the students who have taken in 2014. (population size (N) is very large] n 25 (2015) 16 (2014) X 60 (2015) 50 (2014) Std. 18 (2015) 12 (2014) (a) Test at the 5% significance level that the difference between the mean exam scores from two years is 5 against the alternative that it is not 5 for the independent sample, population variance unknown case. Use v = 40 (b) Illustrate the hypothesis test by using a figure from part (a). You need to include 2 distributions, population mean differences, the critical value, the rejection region and the sample mean difference. (c) Derive p-value for the test from part (a). Use the closest table value. (d) Suppose that 5 students earned "A1" in 2015 and 2 students earned "A1" in 2014 in the samples. Test at 5% significance level that the population proportion of earning A1 is equal for both years against the population proportion for 2015 is greater.