Problem 3. Looking at the midterm grades for one of my courses, I have the following data for 2 separate sections: Section Section 1 Section 2 Problem 3a) Students Enrolled 35 31 Average Grade 65.9 Standard Deviation 54.9 21.4 22.9 I write the following hypotheses that I wish to test: Ho=65 HA: 65 Which of the following best describes what these hypotheses indicate? I wish to test the claim that the average grade on the exam is usually 65 and these results indicate otherwise. I wish to test the claim that the average grade on this exam is not 65 because usually it is. I wish to test the claim that the average grade on this exam is 65 because usually it is some other value. I wish to test the claim that section 2 scored worse on the exam than section 1. Problem 3b) The long term average on this midterm is 65. Based on hypothesis testing, and a significance of 0.01, I can say which of the following about Section 2 Section 2 has a mean closer to 55 than 65 The mean score for Section 2 is not 65 The mean score for Section 2 might be 65. The data do not support the claim that the mean score is not 65. 14 1 point Problem 3c) The long term average on this midterm is 65. Based on hypothesis testing, and a significance of 0.01, I can say which of the following about Section 1 The data support a claim that the mean score is 65. The mean score for Section 1 is greater than the mean score for Section 2 The data do not support either the null or alternative hypotheses. The data do not support a claim that the mean score is different than 65. 15 1 point Problem 3d) A 90% 2-sided confidence interval around the data for Section 1 is closest to which of the following. Use a normal distribution. 65.91.96 65.95.9 65.97.1 65.9 3.6 16 1 point Problem 3e) A 90% 1-sided upper limit confidence interval for the mean of Section 2 is closest to which of the following. Use the t-distribution 60.2 17 1 point 65.0 61.9 49.5 Problem 3f) The two sections seem to have different scores, perhaps suggesting there is indeed a difference between them. The standard t-test, as discussed in class, could have hypotheses written as: He - 0 HA: 14-0 These hypotheses suggest which of the following claims is being made That Section 1 scored higher than Section 2. That Section 2 scored lower than Section 1. OThat the means of the two sections are indeed different. That the means of the two sections are identical. 18 1 point Problem 3g) If a 0.01 significance is considered, the results of a t-test on the means of the two sections indicate: p>0.01, therefore the claim that the 2 sections have different means is supported. P<0.01, therefore the 2 sections likely have the same mean P<0.01, therefore the claim that the 2 sections have different means is supported. Op>0.01, therefore the claim that the 2 sections have different means is not supported.