Question

The standard IQ test has a mean of 102 and a standard deviation of 13. We want to be 98% certain that that we are within 5 IQ points of the true mean. Determine the required sample size.

Answer 1

37

Explanation:

Margin of error = critical value × standard error

For 98% confidence, CV = 2.326 (from t table).

Standard error is σ / √n, where σ is the population standard deviation, and n is the sample size.

Plugging in:

5 = 2.326 × 13 / √n

n = 36.6

Rounding up, n = 37.