An industrial engineer is conducting a time study for a work element. The select time is 7.5 minutes, and the sample standard deviation of the observed time is one minute. What is the appropriate sample size if the estimate is to be 3 percent of the True average time 95 percent of the time (z = 1.96)?
A) fewer than or equal to 70
B) greater than 70 but fewer than or equal to 80
C) greater than 80 but fewer than or equal to 90
D) greater than 90

Question

Quizplus · Accepted Answer

Since we want the estimate to be within 3% of the true average time with 95% confidence, we can use the formula:

n = [(z * σ) / E]^2

where n is the sample size, z is the z-score for the desired level of confidence (1.96 for 95%), σ is the sample standard deviation (1 minute), and E is the maximum allowable error, which is 3% of the select time (0.03 * 7.5 = 0.225).

Plugging in the values:

n = [(1.96 * 1) / 0.225]^2 = 77.44

Since we can't have a fractional number of observations, we round up to the nearest whole number. Therefore, the appropriate sample size is greater than 70 but fewer than or equal to 80, which is choice B.

An Industrial Engineer Is Conducting a Time Study for a Work