Question

The scores of men on the Math SAT follow a normal distribution; so do those of women. It is reasonable to assume that the standard deviation of the two scores is equal. Let μ1 (respectively, μ2) denote the average math SAT score of men (respectively, women). A random sample of 20 men was selected. The average math SAT score of the men selected was 607.8 with a standard deviation of 48.76. Another random sample of 23 women was selected (independently of the sample of men). The average math SAT score of the women selected was 543.71 with a standard deviation of 53.1. Obtain a 94% confidence interval for μ1 - μ2

          The scores of men on the Math SAT follow a normal distribution;
so do those of women. It is reasonable to assume that the standard
deviation of the two scores is equal. Let μ1 (respectively, μ2)
denote the average math SAT score of men (respectively, women). A
random sample of 20 men was selected. The average math SAT score of
the men selected was 607.8 with a standard deviation of 48.76.
Another random sample of 23 women was selected (independently of the
sample of men). The average math SAT score of the women selected
was 543.71 with a standard deviation of 53.1.
Obtain a 94% confidence interval for μ1 - μ2
        
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Added by Sarah S.

Elementary Statistics a Step by Step Approach
Elementary Statistics a Step by Step Approach
Allan G. Bluman 9th Edition
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The scores of men on the Math SAT follow a normal distribution; so do those of women. It is reasonable to assume that the standard deviation of the two scores is equal. Let μ1 (respectively, μ2) denote the average math SAT score of men (respectively, women). A random sample of 20 men was selected. The average math SAT score of the men selected was 607.8 with a standard deviation of 48.76. Another random sample of 23 women was selected (independently of the sample of men). The average math SAT score of the women selected was 543.71 with a standard deviation of 53.1. Obtain a 94% confidence interval for μ1 - μ2
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The scores of men on the Math SAT follow a normal distribution; so do those of women. It is reasonable to assume that the standard deviation of the two scores is equal. Let μ1 (respectively, μ2) denote the average math SAT score of men (respectively, women). A random sample of 20 men was selected. The average math SAT score of the men selected was 607.8 with a standard deviation of 48.76. Another random sample of 23 women was selected (independently of the sample of men). The average math SAT score of the women selected was 543.71 with a standard deviation of 53.1. Obtain a 94% confidence interval for μ1 - μ2

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Transcript

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00:01 Question, we have two populations.
00:01 We have the scores for the men and the scores for the women.
00:06 So basically, we want to test here if we can say that the difference between the scores for the male, so let's say me one, minus the mean of the scores for the women, if this difference is greater than 30, which basically means that the score for the men are like at least 30 points above the scores for the women, the mean score in this case.
00:35 So because we are interested in comparing like the difference of means, we need to compute the test statistic for this kind of problem for the difference of means.
00:45 So here the test statistic is given by this t and it is given by the sample mean for the man minus the sample mean for the women using the sample that they used, minus this number 30.
00:58 Then divide this by the square root here.
01:03 And because we are assuming that the standard deviations or the variances between these two groups or the same, we are going to use this denominator.
01:13 So this denominator here is basically a pooled variance.
01:20 Then we need to divide this by the simple size for the man.
01:25 Then repeat the same variance, considering all the same variance.
01:28 Samples divided by the sample size for the women.
01:34 So first we need to compute this sp square...
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