We want to estimate with 99 percent confidence the percentage of automobile purchasers 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 purchasers 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 for a proportion with a given margin of error and confidence level, we use the formula: 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). Plugging in these values, we find that the required sample size is approximately 523.

We Want to Estimate with 99 Percent Confidence the Percentage