Math/Physic/Economic/Statistic Problems

Name:Case Study #1: Comparing Two Means … 100 points totalAll answers should be typed on this document. You will then save the document and submit it using the submission link in the Case Study #1 folder on Blackboard. Please include your last name in the filename of your document when saving it.For example I would save mine as follows: Steiner Case Study 1.doc1. Does tuning a car engine improve the gas mileage? A sample of 8 automobiles were run todetermine their mileage, in miles per gallon. Then, each car was given a tune-up and runagain to measure the mileage a second time. The results are in the table below. Enter thisdata into two separate columns in Minitab. Sample 1 will be the data for the automobiles\”After Tune-up\” (entered in Column C1) and Sample 2 will be the data for the automobiles\”Before Tune-up\” (entered in Column C2). Then test the claim that the mean mileage is higherafter the tune-up. Use a significance level of 0.05.Automobile1 2 3 4 5 6 7 8After Tune-up 35.44 35.17 31.07 31.57 26.48 23.11 25.18 32.39Before Tune-up 33.76 34.30 29.55 30.90 24.92 21.78 24.30 31.25a. Are these Independent samples or Paired samples? (Highlight the correct choice below.)Independent Pairedb. Highlight the appropriate test to use in Minitab: 2-Sample t Paired tc. Let µd denote the population mean difference After – Before.Write the null and alternative hypotheses: H0: µd ___________ HA: µd ___________d. What is the rejection rule?e. Using Minitab, compute the test statistic?f. Using Minitab, compute the P-value?g. Based on your P-value and rejection rule, what is the conclusion about the null hypothesis?(Highlight the correct conclusion below.)Reject H0 Fail to reject H0h. What do you conclude about the claim that the gas mileage is higher after the tune-up?2.The National Assessment of Educational Progress (NAEP) tested a sample of students who had used a computer in their math classes, and another sample of students who had not used a computer. The sample mean score for students using the computer was 309, with a sample standard deviation of 29. For students not using a computer, the sample mean was 303, with a sample standard deviation of 32. Assume there were 60 students in the computer sample, and 40 students in the sample that hadn\’t used a computer. Can you conclude that the population mean scores differ? Use a significance level of 0.05. Let the sample who used the computer be Sample 1, and the sample that didn\’t use the computer be Sample 2.a. Are these Independent samples or Paired samples? (Highlight the correct choice below.)Independent Pairedb. Highlight the appropriate test to use in Minitab: 2-Sample t Paired tc. Write the null and alternative hypotheses: H0: µ1 – µ2 _______HA: µ1 – µ2 _______d. What is the rejection rule?e. Using Minitab, compute the test statistic?f. Using Minitab, compute the P-value?g. Based on your P-value and rejection rule, what is the conclusion about the null hypothesis?(Highlight the correct conclusion below.)Reject H0 Fail to reject H0h. What do you conclude about the claim that the mean scores differ?https://youtu.be/ZQZcoxTotmc