What is the minimum sample size required to estimate a population mean with 95% confidence when the desired margin of error is E = 1.5? The population standard deviation is known to be 10.75.
A) n = 138
B) n = 139
C) n = 197
D) n = 198

Question

Quizplus · Accepted Answer

To estimate the minimum sample size required to estimate a population mean with a specific confidence level, the formula is $n = \left(\frac{Z \cdot \sigma}{E}\right)^2$, where $Z$ is the Z-score corresponding to the confidence level, $\sigma$ is the population standard deviation, and $E$ is the desired margin of error. For a 95% confidence level, the Z-score is approximately 1.96. Plugging in the values: $n = \left(\frac{1.96 \cdot 10.75}{1.5}\right)^2 \approx 197.6$. Since the sample size must be a whole number, we round up to the nearest whole number, which is 198.

What Is the Minimum Sample Size Required to Estimate a Population