We want to estimate with 99 percent confidence the percentage of buyers of cars who are under 30 years of age.A margin of error of 5 percentage points is desired.What sample size is needed? In an earlier sample we found a 99 percent confidence interval of buyers under 30 years of age to be [.18 .27].
A)104
B)664
C)392
D)523

Question

Quizplus · Accepted Answer

To determine the sample size needed for a given margin of error and confidence level, we use the formula for sample size in proportion estimation: n = (Z^2 * p * (1-p)) / E^2. Here, Z is the Z-score for 99% confidence (approximately 2.576), p is the estimated proportion (average of the interval, (0.18+0.27)/2 = 0.225), and E is the margin of error (0.05). Calculating this gives approximately 523.

We Want to Estimate with 99 Percent Confidence the Percentage