2. MATH 233 has two sections. Final scores of 50 randomly selected TEDU students in Section...

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2. MATH 233 has two sections. Final scores of 50 randomly selected TEDU students in Section 1 are as follows. 83 45 88 63 86 61 100 64 76 86 62 93 51 88 89 73 80 86 76 78 45 85 56 71 47 60 84 100 89 52 97 84 67 51 72 70 60 56 95 91 50 47 99 70 84 62 48 51 55 52 Similarly, the final scores of 60 randomly selected TEDU students in Section 2 are as follows. 77 71 98 86 68 54 94 65 65 87 82 88 70 65 78 72 97 66 84 81 93 100 52 74 72 98 87 58 92 71 60 54 64 76 95 83 76 72 90 84 87 62 76 67 72 84 63 91 56 53 94 63 90 53 83 99 97 54 65 a) (2 pts) Obtain the point estimate of the proportion of Section 1 students receiving a final score of 75 or more at TEDU. b) (2 pts) Obtain the point estimate of the proportion of Section 2 students receiving a final score of 75 or more at TEDU. c) (8 pts) Construct a 95% two-sided confidence interval on the difference between the proportions of Section 1 and Section 2 receiving final scores of 75 or more at TEDU. d) (8 pts) Is it plausible to consider that both sections have the same proportion of having at least 75 in terms of the final scores of MATH 233? Conduct a hypothesis test to check this claim. Use P-value approach and take 5% significance level. 2. MATH 233 has two sections. Final scores of 50 randomly selected TEDU students in Section 1 are as follows. 83 45 88 63 86 61 100 64 76 86 62 93 51 88 89 73 80 86 76 78 45 85 56 71 47 60 84 100 89 52 97 84 67 51 72 70 60 56 95 91 50 47 99 70 84 62 48 51 55 52 Similarly, the final scores of 60 randomly selected TEDU students in Section 2 are as follows. 77 71 98 86 68 54 94 65 65 87 82 88 70 65 78 72 97 66 84 81 93 100 52 74 72 98 87 58 92 71 60 54 64 76 95 83 76 72 90 84 87 62 76 67 72 84 63 91 56 53 94 63 90 53 83 99 97 54 65 a) (2 pts) Obtain the point estimate of the proportion of Section 1 students receiving a final score of 75 or more at TEDU. b) (2 pts) Obtain the point estimate of the proportion of Section 2 students receiving a final score of 75 or more at TEDU. c) (8 pts) Construct a 95% two-sided confidence interval on the difference between the proportions of Section 1 and Section 2 receiving final scores of 75 or more at TEDU. d) (8 pts) Is it plausible to consider that both sections have the same proportion of having at least 75 in terms of the final scores of MATH 233? Conduct a hypothesis test to check this claim. Use P-value approach and take 5% significance level.

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