An instructor would like to investigate the possibility of a difference in STAT 2001 final scores...

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An instructor would like to investigate the possibility of a difference in STAT 2001 final scores between male (population 1) and female (population 2) students. 62 students were classified into male (sample 1) and female (sample 2) categories, and their STAT 2001 final scores are provided below. Assume these two samples are simple random samples selected from normally distributed populations. Male Female 85.6 90.4 85.5 75.0 98.9 69.1 92.8 54.8 87.2 96.0 80.9 93.7 83.0 82.3 65.2 82.8 91.4 74.3 87.2 98.5 48.3 91.5 94.2 87.6 87.0 88.6 94.3 98.8 91.7 93.7 90.6 84.2 86.2 92.9 75.0 97.8 94.3 96.0 95.0 83.1 54.5 78.8 96.7 91.5 99.2 64.9 95.7 97.2 100.0 83.3 94.3 99.0 79.1 93.0 87.2 88.0 98.5 96.5 89.6 98.6 93.4 82.7 (A). Calculate the sample sizes (n₁ and n₂), sample means (₁ and ₂) and sample variances (s2 and s2). Round the final answers to two decimal points. (3 marks) (B). At the 5% level of significance, conduct an appropriate hypothesis test to test a difference between the mean final scores of male and female students. Use the P-value approach and show all the steps. (4 marks) (C). Suppose we had instead used the classical approach to conduct the test in (B). What would be the decision/rejection rule of the test? (1 mark) (D). Construct a 95% confidence interval for the difference between the mean final scores of male and female students. Round the final answers to two decimal points. (2 marks) An instructor would like to investigate the possibility of a difference in STAT 2001 final scores between male (population 1) and female (population 2) students. 62 students were classified into male (sample 1) and female (sample 2) categories, and their STAT 2001 final scores are provided below. Assume these two samples are simple random samples selected from normally distributed populations. Male Female 85.6 90.4 85.5 75.0 98.9 69.1 92.8 54.8 87.2 96.0 80.9 93.7 83.0 82.3 65.2 82.8 91.4 74.3 87.2 98.5 48.3 91.5 94.2 87.6 87.0 88.6 94.3 98.8 91.7 93.7 90.6 84.2 86.2 92.9 75.0 97.8 94.3 96.0 95.0 83.1 54.5 78.8 96.7 91.5 99.2 64.9 95.7 97.2 100.0 83.3 94.3 99.0 79.1 93.0 87.2 88.0 98.5 96.5 89.6 98.6 93.4 82.7 (A). Calculate the sample sizes (n₁ and n₂), sample means (₁ and ₂) and sample variances (s2 and s2). Round the final answers to two decimal points. (3 marks) (B). At the 5% level of significance, conduct an appropriate hypothesis test to test a difference between the mean final scores of male and female students. Use the P-value approach and show all the steps. (4 marks) (C). Suppose we had instead used the classical approach to conduct the test in (B). What would be the decision/rejection rule of the test? (1 mark) (D). Construct a 95% confidence interval for the difference between the mean final scores of male and female students. Round the final answers to two decimal points. (2 marks)