Question

We want to estimate the proportion of students who have credit card debt more than $2,000. What size sample should be obtained if we want to estimate the proportion within 3%; that is, the margin of error is 3%, with 95% confidence.

a) suppose a prior study indicates that the percentage is 30%

b) suppose we use no prior estimate of the percentage.

Answer 1

Z for 95% confidence interval = Z_0.025 = 1.96

A) Margin of error = Z * sqrt(p * (1-p) / n)

Or, 0.03 = 1.96 * sqrt (0.3 * 0.7 / n)

Or, n = 897

B) 0.03 = 1.96 * sqrt(0.5 * 0.5 / n)

Or, n = 1068