Educational Research plans a study to estimate the length of the average workweek for faculty members at public universities by taking a simple random sample of this group.If you want to insure a 90% probability that the sample mean you produce will be no more than 1 hour away from the actual population mean, how large a sample should you select for your study.Based on previous experience, you estimate a population standard deviation of approximately 12 hours.
A)315
B)392
C)342
D)487
E)429

Question

Quizplus · Accepted Answer

To determine the sample size needed to estimate the population mean with a specific margin of error (E) at a certain confidence level, you can use the formula for the sample size $n$ in estimating a mean with a normal distribution: $n = \left(\frac{Z \cdot \sigma}{E}\right)^2$, where $Z$ is the Z-score corresponding to the desired confidence level (for 90% confidence, $Z \approx 1.645$), $\sigma$ is the population standard deviation, and $E$ is the margin of error. Plugging in the values given ($\sigma = 12$ hours and $E = 1$ hour), we get $n = \left(\frac{1.645 \cdot 12}{1}\right)^2 = \left(\frac{19.74}{1}\right)^2 \approx 392$. Therefore, a sample size of approximately 392 is needed.

Educational Research Plans a Study to Estimate the Length of the Average