Open the next tab titled “MAT152HT-TestData” and use it to complete the questions below. This tab contains sample data for a random group of 41 MAT 152 students from previous semesters. For Tests 1 and 2, both the scores and the completion times were recorded for each student. For Test 3, only the scores were recorded. (Student names are fake to protect privacy, but the times and scores are real.) For full credit, you must show all work including the hypotheses (label the claim), a sketch or description of the sampling distribution indicating the direction of the test, test statistic, and P-value. You must also state your decision, and separately, give an interpretation in the context of the original claim. Use a different font color (other than black) for your answers. Problems 1. An instructor was evaluating Test 1 and was very pleased with the results. She said to her coworker, “I think the grades for Test 1 were very good. I’m willing to bet the average overall score for this test is higher than a 75.” Test the instructor’s claim that the population mean score for Test 1 is higher than 75. Use a level of significance of 0.01. (30 pts) 2. If your decision for the hypothesis test you performed for Problem 1 was incorrect, what type of error would it be (Type I or Type II)? Identify the type of error. Then, explain what this error would mean in the context of this situation. (10 pts) 3. After Test 1, several instructors talked with one another about the difference in times for Test 1 and Test 2. One instructor said, “Test 2 seemed longer than Test 1. I’d estimate Test 2 was longer than Test 1 by an average of 10 minutes." Use a significance level of 0.10 to test the instructor’s claim that, on average, Test 2 was 10 minutes longer than Test 1. (30 pts) 4. A student looked back on the three tests at the end of the semester and speculated, “I think the hardest test was Test 2. In fact, I think that students scored better on Test 2 than Test 3 .” Use a level
