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

To determine the appropriate sample size, we use the formula:

n = (z * s / E)^2

Where
z = 1.96 (from the 95% confidence interval)
s = 1 minute (sample standard deviation)
E = 0.03 * 7.5 = 0.225 minutes (desired margin of error)

Plugging in the values, we get:

n = (1.96 * 1 / 0.225)^2 ≈ 78.7

Rounding up to the nearest whole number, the appropriate sample size is 79. Therefore, the best choice is B (greater than 70 but fewer than or equal to 80).

An Industrial Engineer Is Conducting a Time Study for a Work