We intend to estimate the average driving time of a group of commuters. From a previous study, we believe that the average time is 42 minutes with a standard deviation of 12 minutes. We wantour 99 percent confidence interval to have a margin of error of no more than plus or minus 3 minutes. What is the smallest sample size that we should consider?
A) 11
B) 319
C) 9
D) 107

Question

Quizplus · Accepted Answer

To find the smallest sample size, use the formula for margin of error in a confidence interval: ME = Z * (σ/√n). For a 99% confidence interval, Z is approximately 2.576. Solving for n gives n = (Z * σ / ME)^2 = (2.576 * 12 / 3)^2 = 107.29, which rounds up to 107.

We Intend to Estimate the Average Driving Time of a Group