Question

Part 1).

A pension analyst wishes to estimate the mean age at which federal employees retire. What sample size is needed if the analyst desires that the width of the confidence interval for a 95% CI for the true mean age is not greater than 1 year? (Based on previous studies, she assumes the population standard deviation is 3.5.)

Part 2).

After completing this calculation, the analyst wishes to understand how different factors influence the sample size calculation for this type of problem. Which of her statements are correct? Briefly explain your reasoning.

a) The required sample size is directly proportional to the population variance.
b) The required sample size is inversely proportional to half the width of the desired confidence interval.
c) The required sample size is directly proportional to the square of the z critical value z_a/2.

Answer 1

1) E = Width/2 = 1/2 = 0.5

For 95% CI, z = 1.96

Population SD = 3.5

Hence,

Sample size required

n = 189

Part 2: From the formula used in part a):

The required sample size is directly proportional to the population variance.

The required sample size is directly proportional to the square of the z critical value z_a/2.

Option A and Option C are correct.