QUESTION 2 a) A report prepared by the Academic Affair Department of Star College claimed that the average, students spent three hours per day studying with the variance of 0.17 hours?. However, one of the deans at the college believed that the mean study hours is actually more than three hours per day. To investigate this claim, the dean carried out a survey. A random sample of 20 students has an average of study hours is 3.32. At 1% significance level, do the data contradict with the dean's claim? (5 marks) b) The number of pushups completed by a sample of nine athletes before and after a stamina- building program was recorded. The data was analysed using SPSS and the result is as follows. Assume that the number of pushups is normally distributed. Paired Samples Test Paired Differences 95% Confidence Interval of the Difference Std. Std. Error df Sig. (2- Mean Deviation Mean Lower Upper tailed) Pair Before- P 1 After -1.667 2.000 667 -3.204 -.1.29 -2.500 .037 i. Based on the p-value, is there is sufficient evidence to indicate that the number of pushups has increased after the stamina-building program. Use a=0.05. (4 marks) ii. State the Type I and Type II error in the context of the test in i). (2 marks)