A time study analyst has found the select time for a work element to be 14.0 minutes, with a sample standard deviation of 3.2 minutes. What is the minimum sample size needed if the estimate is to be within 4 percent of the average 95 percent of the time (z = 1.96)?
A) fewer than 100
B) greater than or equal to 100 but fewer than 140
C) greater than or equal to 140 but fewer than 180
D) greater than or equal to 180

Question

Quizplus · Accepted Answer

The minimum sample size needed can be calculated using the formula for the sample size in estimating a population mean with a specific confidence level: $n = \left(\frac{z \cdot \sigma}{E}\right)^2$, where $n$ is the sample size, $z$ is the z-score corresponding to the confidence level (1.96 for 95% confidence), $\sigma$ is the standard deviation, and $E$ is the margin of error. The margin of error is given as a percentage of the mean, so $E = 0.04 \times 14 = 0.56$ minutes. Plugging in the values: $n = \left(\frac{1.96 \cdot 3.2}{0.56}\right)^2 \approx 121$. Therefore, the sample size must be greater than or equal to 100 but fewer than 140.

A Time Study Analyst Has Found the Select Time for a Work