A retailer wants to estimate with 99% confidence the number of people who buy 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

The minimum sample size necessary for estimating a population proportion with a certain level of confidence and margin of error can be calculated using the formula: $n = \left(\frac{Z^2 \cdot p \cdot (1-p)}{E^2}\right)$, where $Z$ is the Z-score corresponding to the desired confidence level, $p$ is the estimated proportion (in this case, 0.24), and $E$ is the desired margin of error (in this case, 0.03). Without calculating the exact number, the statement provides a specific sample size (1,100) without showing the calculation or the Z-score used for a 99% confidence level, which typically would be approximately 2.576. The actual calculation might yield a different result than 1,100, depending on these factors.

A Retailer Wants to Estimate with 99% Confidence the Number