Very basic stats-hyphothsis, confidence interval problem. Please solve this with steps, thanks!

As a researcher, your goal is to estimate the effect of a drug on the test scores of human subjects undertaking a test in Statistics. All subjects were divided into two populations X and Y, with members of population X receiving the drug prior to testing and members of population Y receiving a placebo prior to testing. 9 subjects were chosen randomly from population X and the mean score in this group was equal to 9.78, with the sample variance being 17.64. Another group of 16 subjects, chosen randomly from population Y, was used as a control group and had the mean score of 15.1, with the sample variance of 27.1. Assume that test scores in both populations are distributed as normal with X N N (,LLX, 03:) and Y N N (una), where MX: ,uy are unknown population means and 0%, 032/ are unknown population variances. Note: you will need to use computer software (Excel, Stata) or scientic calculators to obtain exact answers to some of the questions below. 1. Suppose your colleague has provided you with the values for the true population variances: a; = 25 and 0% = 36. Using this information, calculate (a) 90% condence interval for MX3 (b) 90% condence interval for 'My: (c) pvalue of a hypothesis test of H0 : x 2 8 vs Ha : pLX 25 : (c) pvalue of a hypothesis test of H0 : a; = 25 vs Ha : 0% > 25 : (d) pvalue of a hypothesis test of H0 : 0% = 36 vs Ha : 032/ > 36 : 3. Given your own ndings regarding a; and 0%, you decide to disregard your colleague's suggestion regarding the true values of a; and 03/. Instead, you decide to treat them as unknown. Calculate (a) 90% condence interval for ,uX: (b) 90% condence interval for 'My: (0) pvalue of a hypothesis test of H0 : ,uX = 8 vs Ha : ,uX