The Hilbert Drug Store owner plans to survey a random sample of his customers with the objective of estimating the mean dollars spent on pharmaceutical products during the past three months. He has assumed that the population standard deviation is known to be $15.50. Given this information, what would be the required sample size to estimate the population mean with 95 percent confidence and a margin of error of ±$2.00?
A) 231
B) 163
C) 16
D) 15

Question

Quizplus · Accepted Answer

To calculate the required sample size for estimating the population mean with a specific confidence level and margin of error when the population standard deviation is known, the formula is: $n = \left(\frac{Z \cdot \sigma}{E}\right)^2$, where $n$ is the sample size, $Z$ is the Z-score corresponding to the confidence level (for 95% confidence, $Z = 1.96$), $\sigma$ is the population standard deviation ($15.50), and $E$ is the margin of error ($2.00). Plugging in the values: $n = \left(\frac{1.96 \cdot 15.50}{2}\right)^2 \approx 231$.

The Hilbert Drug Store Owner Plans to Survey a Random