A time study analyst is determining the standard time for a work element. The select time is 6.0 minutes, and the standard deviation of the select time is 2.2 minutes, based on a pilot sample of 20 observations. What is the appropriate sample size if the estimate for the select time is to be within 10 percent of the True average time 95 percent of the time (z = 1.96)?
A) fewer than 30 observations
B) greater than or equal to 30 observations but fewer than 40 observations
C) greater than or equal to 40 observations but fewer than or equal to 50 observations
D) greater than or equal to 50 observations

Question

Quizplus · Accepted Answer

To calculate the appropriate sample size, we use the formula:
n = (z*σ/E)^2
where,
z = 1.96 (from the 95% confidence level)
σ = 2.2 (standard deviation of select time)
E = 0.1*6.0 (10% of the select time)
n = sample size

Plugging in the values, we get:
n = (1.96*2.2/(0.1*6.0))^2
n = 50.74

Therefore, we need a sample size of at least 51 observations to obtain an estimate for the select time that is within 10% of the true average time, 95% of the time. The closest answer choice is D, which is greater than or equal to 50 observations.

A Time Study Analyst Is Determining the Standard Time for a Work