VI In the following study educational researchers were interested in whether a New Method for teaching mathematics was more effective than the Standard Method. A sample of n = 20 students were taught by the Standard Method, while another sample of m = 15 students were taught by the New Method. Each student was given a mathematics proficiency test at the end of the teaching period. The scores on this test are tabulated below: 76.1 55.8 67.3 73.9 67.3 73.9 71.4 Standard Method New Method 54.2 61.9 69.2 76.4 69.6 66.0 81.1 66.6 77.2 77.5 70.3 63.2 33.4 55.6 42.0 37.9 23.7 14.5 26.6 55.2 89.9 85.4 66.3 67.9 13.8 10.7 36.9 71.6 Some Summary Statistics are given below: n Standard Method 20 1417.4 101932.70 New Method 15 632.9 33669.55 Stat 245.3(02) Final Examination April 2023 56. Determine 99% confidence limits for the mean of math proficiency scores of students taught by the Standard Method. a) 68.84 to 72.9 b) f) 66.58 to 75.16 g) 68.38 to 73.36 66.12 to 75.62 c) 67.93 to 73.81 d) h) 65.67 to 76.07 i) 67.48 to 74.26 e) 67.03 to 74.71 65.22 to 76.52 j) 64.77 to 76.97 57. Determine 99% confidence limits for the mean of math proficiency scores of students taught by the New Method. a) 34.07 to 50.31 b) f) 25.05 to 59.34 g) 32.27 to 52.12 23.24 to 61.14 c) 30.46 to 53.92 d) h) 21.44 to 62.95 i) 28.66 to 55.73 e) 26.85 to 57.53 19.64 to 64.75 j) 17.83 to 66.56 58. Determine 95% confidence limits for the standard deviation () of math proficiency scores of students taught by the Standard Method. a) 1.27 to 8.77 b) 2.11 to 24.52 c) 6.72 to 12.9 d) 12.21 to 20.03 e) 11.22 to 31.67 f) 16.33 to 35.18 g) 0.35 to 27.46 h) 8.68 to 28.66 59. Determine 95% confidence limits for the standard deviation () of math proficiency scores of students taught by the New Method. a) 1.27 to 8.77 b) 2.11 to 24.52 c) 6.72 to 12.9 e) 11.22 to 31.67 f) 16.33 to 35.18 g) 0.35 to 27.46 d) 12.21 to 20.03 h) 8.68 to 28.66 60. Determine 99% confidence limits for the difference in means between math proficiency scores of students taught by the Standard Method and math proficiency scores of students taught by the New Method. Assume equal population variances. a) 22.84 to 34.51 f) 16.36 to 40.99 b) 21.55 to 35.81 g) 15.06 to 42.29 c) 20.25 to 37.1 d) 18.95 to 38.4 h) 13.77 to 43.59 i) 12.47 to 44.88 e) 17.66 to 39.7 j) 11.17 to 46.18 The End