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?

Box 1: Enter your answer as an integer or decimal number. Examples: 3, -4, 5.5172
Enter DNE for Does Not Exist, oo for Infinity

Answer 1

We calculate sample size by rearranging the basic calculation of Z for the sample mean:

Z = (x-bar - μ) / (σ/sqrt(n))

Since our margin of error (E) is the allowable difference between the sample mean and the population mean, we make that our denominator:

Z = E/ (σ/sqrt(n))

A little algebra gives us

sqrt(n) = z*σ/E

We square both sides, giving us

n = (z*σ/E)^2

Now since we want a 95% confidence interval, we know that Z = 1.96. Therefore we have all the numbers we need and can just plug them in.

n = (1.96*300/25)^2

= (1.96*12)^2

=553.19

=554