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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. Sixty-two 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 Scores:**
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, 65.2, 82.8, 91.4, 74.3, 87.2, 98.5, 91.5, 94.2, 87.6, 87.0, 58.6, 94.3, 96.8, 91.7, 93.7, 90.6, 84.2

**Female Scores:**
86.2, 92.9, 75.0, 97.8, 94.3, 96.0, 95.0, 83.1, 84.5, 78.8, 96.7, 91.5, 99.2, 64.9, 95.7, 97.3, 100.0, 83.3, 94.3, 99.0, 79.1, 93.0, 87.2, 88.0, 98.5, 96.5, 89.5, 98.6, 93.4, 82.7

**Task:**
(A) Calculate the sample sizes (\( n_1 \) and \( n_2 \)), sample means (\( \bar{x}_1 \) and \( \bar{x}_2 \)), and sample variances (\( s_1^2 \) and \( s_2^2 \)). Round the final answers to two decimal points.

Answer :

Final answer:

The sample sizes, means, and variances for the male and female categories are calculated from the given data.

Explanation:

To calculate the sample sizes, means, and variances, we need to analyze the given data for both male and female categories. For the male sample, there are 22 values, so the sample size (n1) is 22. The sample mean (ν1) is calculated by summing all the values and dividing by the sample size. For the male sample, the sample mean is 85.63. To calculate the sample variance (1), the squared differences between each data value and the sample mean are summed and divided by the sample size minus 1. For the male sample, the sample variance is 147.49. Repeat the same process for the female sample to find n2, ν2, and 2. The female sample has 30 values, so n2 is 30. The sample mean for the female sample is 90.70. The sample variance is 79.59.

Learn more about Calculating sample statistics here:

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