How many cycles should be used in a time study in order to be 98% confident that the time-study average job cycle time is within 4% of the true average job cycle time.Assume that the average job cycle time was 4.25 minutes and the standard deviation of the sample was 0.65 minutes.
A)55 cycles
B)70 cycles
C)80 cycles
D)95 cycles

Question

Quizplus · Accepted Answer

To calculate the number of cycles required for the time study, we use the formula:

n = [(z*s/E)^2]*(1-p)/(p)

where, 
n = number of cycles to be used in the time study
z = Z-score for desired level of confidence (in this case, 2.33 for 98% confidence)
s = sample standard deviation (0.65 minutes)
E = acceptable margin of error (0.04 * 4.25 = 0.17 minutes)
p = proportion of defective items (we assume p = 0.5 as there are no defects in this case)

Substituting the values in the formula, we get:

n = [(2.33*0.65/0.17)^2]*(1-0.5)/(0.5)
n = 79.74
Rounding up to the nearest integer, the number of cycles required for the time study is 80.

Therefore, the best choice is C) 80 cycles as it is the closest integer value to the calculated value of n.

How Many Cycles Should Be Used in a Time Study