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

Question

We want to estimate the mean change in score µ in the population of all high school seniors. An SRS of 350 high school seniors gained an average of xx¯ = 22 points in their second attempt at the SAT Mathematics exam. Assume that the change in score has a Normal distribution with standard deviation 45.883. Find xx¯, the standard deviation of the mean change 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

Solution:-

Given, n = 350

Mean x-bar = 22

Standard deviation = 45.883

Find xbar, the standard deviation of the mean change xbar _____ (±0.001).

45.883 / sqrt(350) = 2.4525

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

Xbar = 22, = 45.883 and n = 1350

X ± {Z*(/sqrt(n))} = 22 ± 1.96 × 2.4525

= [17.1931 , 26.8069]

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