A retailer wants to estimate with 99% confidence the number of people who shop at his
store. A previous study showed that 24% of those interviewed had shopped at his store.
He wishes to be accurate within 3% of the true proportion. The minimum sample size
necessary would be 1,100.

Question

Quizplus · Accepted Answer

To estimate the minimum sample size necessary for a given confidence level and margin of error, the formula is $n = \frac{Z^2 \cdot p \cdot (1-p)}{E^2}$, where $Z$ is the Z-score corresponding to the desired confidence level (for 99% confidence, $Z \approx 2.576$), $p$ is the estimated proportion (0.24 in this case), and $E$ is the margin of error (0.03). Plugging these values in gives a different number than 1,100, indicating that the statement is false.

A Retailer Wants to Estimate with 99% Confidence the Number