An industrial engineer is conducting a time study for a work element.The select time is 4.5 minutes,and the sample standard deviation of the observed time is 20 seconds.What is the appropriate sample size if the estimate is to be 5 percent of the true average time 95 percent of the time?
A) Fewer than or equal to seven
B) Greater than seven but fewer than or equal to eight
C) Greater than eight but fewer than or equal to nine
D) Greater than nine

Question

Quizplus · Accepted Answer

The formula for sample size calculation for mean time estimation is given by:

n = [(zα/2 × σ) / E]^2

Where, 
zα/2 = 1.96 from standard normal table for 95% confidence level
σ = 20 seconds
E = 0.05 × 4.5 minutes = 0.225 minutes = 225 seconds (as 1 minute = 60 seconds)

Plugging in the values, we get:

n = [(1.96 × 20) / 225]^2 = 8.74

Since the sample size needs to be a whole number, we round up to the next integer, which is 9. Therefore, the appropriate sample size is greater than eight but fewer than or equal to nine, which is choice C.

An Industrial Engineer Is Conducting a Time Study for a Work