Question 5 [25 marks]. Lecturers at a university intend to see the effect of stress relief strategies such as deep breathing and relaxation techniques to the student performance in the final exam. For this reason, they assigned students of the same year in two different cohorts. More precisely, students in Cohort 1 did not do any relaxation techniques before the exam, while students in Cohort 2 performed a full range of the relaxation techniques approved by the British Psychological Society. The average mark of a random sample of 17 students from Cohort 1 was 61, with a standard deviation of 17, while the average mark of a random sample of 11 students from Cohort 2 was 67 with a standard deviation of 19. (a) Test whether the variances of marks for the two cohorts are the same at the 5% significance level. [7] (b) Test the hypothesis that the average mark in the exam for Cohort 1 students is the same as that for students of Cohort 2 at the 5% significance level. For this test, what is the p-value? [9] (c) What does the p-value that you calculated in (b) indicate about the null hypothesis? [2] (d) Calculate a 95% confidence interval for the difference in average marks in the exam for the two cohorts of students. Explain the meaning of the 95% confidence interval that you have calculated. NB. In your answers to all the questions above, report the numerical computations to three decimal places. [7]