The accuracy of a labor standard is to be within 5%, and the confidence level is 95%. The standard deviation of the sample is 2 and the mean is 8. What sample size should be used?
A) 8
B) 10
C) 96
D) 127
E) cannot be determined from the information given

Question

Quizplus · Accepted Answer

To determine the sample size needed for a specific accuracy and confidence level, you can use the formula for the sample size in estimating a mean with a specified precision: $n = \left(\frac{Z \cdot \sigma}{E}\right)^2$, where $Z$ is the Z-score corresponding to the desired confidence level (for 95%, $Z = 1.96$), $\sigma$ is the standard deviation, and $E$ is the desired margin of error (accuracy). Here, $E = 5\% \times 8 = 0.4$. Plugging in the values: $n = \left(\frac{1.96 \cdot 2}{0.4}\right)^2 = \left(\frac{3.92}{0.4}\right)^2 = \left(9.8\right)^2 = 96.04$, which rounds to 96.

The Accuracy of a Labor Standard Is to Be Within