If you would like to limit the margin of error of your 95% confidence interval to 25 points, how many students should you sample?

Question

SAT scores are distributed with a mean of 1,500 and a standard deviation of 300. You are interested in estimating the average SAT score of first year students at your college. If you would like to limit the margin of error of your 95% confidence interval to 25 points, how many students should you sample?

Make sure to give a whole number answer.

Answer 1

z-critical for 95 CI is 1.96

standard deviation is given as 300

ME is given as 25

ME = z-critical * standard deviation/sqrt(sample size)

ME * sqrt(sample size) = z-critical * standard deviation

sqrt(sample size) = z-critical * standard deviation/ME

sample size = (z-critical * standard deviation/ME)^2

substituting

sample size = (1.96 * 300/25)^2 = 553.19 --> 554