Question 9 Working this problem. Your answer is CORRECT. This is a written question, worth 17 points. DO NOT place the problem code on the answer sheet. A proctor will fill this out after exam submission. Show all steps (work) on your answer sheet for full credit. Problem Code: 978 The table below gives the pretest and post test scores on the MLA's listening test in Spanish for 10 high school Spanish teachers who attended an intensive summer course in Spanish. Teacher Pre-test Post-test 1 30 29 2 30 32 3 28 31 4 24 25 5 29 31 6 30 31 7 34 32 8 32 33 9 28 28 10 16 20 Part a: We hope to show that attending the institute improves listening skills. State the hypotheses. Part b: Perform the significance test on your hypothesis. Report the test statistic and p-value. State your conclusion in terms of the issue. Part c: Give a 90% confidence interval for the mean increase in listening score due to attending the summer institute. a) I have placed my work and my answer on my answer sheet. b) I want to have points deducted from my test for not working this problem. Question 10 Your answer is CORRECT. This is a written question, worth 17 points. DO NOT place the problem code on the answer sheet. A proctor will fill this out after exam submission. Show all steps (work) on your answer sheet for full credit. Problem Code: 1012 The belief is that the mean number of hours per week of part-time work of high school seniors in a city is 10.5 hours. Data from a simple random sample of 22 seniors indicated that their mean number of part-time work was 12.3 with a standard deviation of 1.3. Test whether these data cast doubt on the current belief. (use = 0.05) Part a: State your null and alternative hypotheses. Part b: Sketch the rejection region. Part c: Calculate the test statistic. Plot this value in your sketch in part b. Part d: Determine the P-value for your test. Part e: State your conclusions clearly in complete sentences. a) I have placed my work and my answer on my answer sheet. b) I want to have points deducted from my test for not working this problem.