Joshua teaches an SAT preparation class where each student takes a pre-test on the first day of class and a post-test on the last day of class. Here are summary statistics for the scores of a recent group of students:

| Test | Mean | Standard Deviation |
|------------|------|--------------------|
| Pre-test | 1000 | 175 |
| Post-test | 1150 | 190 |

Let \( D \) represent the difference between a randomly chosen student's pre- and post-test scores. Find the standard deviation of \( D \).

The standard deviation of the differences between a student's pre- and post-test scores in an SAT preparation class is calculated with the formula for the standard deviation of two independent variables. In this case, the standard deviation is approximately 258.32

Explanation:

In this question it is asked to calculate the standard deviation of the difference (D) of the pre- and post-test scores for a student's SAT preparation class. To calculate this, one should use the formula for the standard deviation of the difference of two independent variables where the variances are added. The variance is the square of the standard deviation. In this case, the standard deviations given for the pre-test and post-test are 175 and 190 respectively.

First, find the variance for both tests by squaring the standard deviations: 1752 = 30625 and 1902 = 36100. Add these two variances to get the variance of D: 30625 + 36100 = 66725. Finally, find the standard deviation of D by taking the square root of the variance of D: √66725 = about 258.32.

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azaleawithrow azaleawithrow · Answer 2 · 2024-07-28T09:27:46-04:00

azaleawithrow azaleawithrow

28-07-2024

Answer:

Cannot be determined

Step-by-step explanation:

The scores are not independent

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