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Dearest reader, twenty-two people compare their ratings of the first and final episodes of Netflix's original smash hit Bridgerton (Season 2) to determine whether character development leads to higher ratings. If the estimated variance of the population of difference scores is 69.22, approximately what is the standard error of the distribution of sample difference scores? 6.72 1.77 16.85 3.41

Question

Dearest reader, twenty-two people compare their ratings of the first and final episodes of Netflix's original smash hit Bridgerton (Season 2) to determine whether character development leads to higher ratings. If the estimated variance of the population of difference scores is 69.22, approximately what is the standard error of the distribution of sample difference scores? 6.72 1.77 16.85 3.41

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Solution

The standard error of the distribution of sample difference scores can be calculated using the formula for the standard error of the mean, which is the standard deviation divided by the square root of the sample size.

In this case, the standard deviation is the square root of the variance, and the sample size is the number of people comparing their ratings.

Step 1: Calculate the standard deviation. The standard deviation is the square root of the variance. So, sqrt(69.22) = 8.32.

Step 2: Calculate the standard error. The standard error is the standard deviation divided by the square root of the sample size. So, 8.32 / sqrt(22) = 1.77.

Therefore, the standard error of the distribution of sample difference scores is approximately 1.77.

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