A company conducted a single sample of a time study for 10 cycles of a job and if the average cycle time was 0.60 minutes,and the standard deviation of the sample was 0.075 minutes,for the company to be 95% confident that the average time computed for the time study is within 5% of the true average cycle time,the time study would need to encompass
A)16 cycles
B)20 cycles
C)24 cycles
D)32 cycles

Question

Quizplus · Accepted Answer

To determine the number of cycles required for the time study to be 95% confident that the average time computed is within 5% of the true average cycle time, we can use the formula:

n = [(z*σ)/E]^2

where:
n = sample size
z = z-score for the desired level of confidence (in this case, 1.96 for 95% confidence)
σ = standard deviation of the sample
E = margin of error (5% of the true average cycle time, or 0.05*μ)

Substituting the given values, we get:

n = [(1.96*0.075)/0.05*0.6]^2
n = 23.53

Since we cannot have a fractional number of cycles, we round up to 24 cycles. Therefore, the best choice is C) 24 cycles.

A Company Conducted a Single Sample of a Time Study