We want to estimate the mean change in score in the population of all high schoo

Question

We want to estimate the mean change in score in the population of all high school seniors. An SRS of 430 high school seniors gained an average of  x¯¯¯x¯ = 23 points in their second attempt at the SAT Mathematics exam. Assume that the change in score has a Normal distribution with standard deviation 45.816.

Find x¯¯¯x¯, the standard deviation of the mean change x¯¯¯x¯.   (±±0.001).

Using the 68-95-99.7 Rule (Empirical Rule), give a 95% confidence interval for based on this sample.

Confidence interval (±±0.001) is between  and

Explanation / Answer

standard deviation of the mean change =45.816/(430)1/2 =2.209

hence from empirical rule: 5% confidence interval for =sample mean -/+2*std deviation of mean

=23 -/+ 2*2.209 =18.582 ; 27.418

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