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?

Answer 1

Solution:
Given in the question
SAT Scores are distributed with
Mean () = 1500
Standard deviation() = 300
Margin of error (E) = 25
Sample size (n) can be calculated as
n = (Zalpha/2 * /E)^2
Confidence level = 0.95
Level of significance () = 1 - 0.95 = 0.05
/2. = 0.05/2 = 0.025
From Z table we found Zalpha/2 = 1.96
So Sample size (n) = (Zalpha/2 * /E)^2 = (1.96*300/25)^2 = 553.1904 or 554
So If you would like to limit the margin of error of your 95% confidence interval to 25 points, 554 Students you should sample.