A work sampling study is being conducted on a loading machine in a warehouse.How many observations should be taken if management wants to be 95% confident the estimate is within +6% of the actual proportion of time the loader is busy if management believes the loading machine is in use 70% of the time?
A)125 observations
B)175 observations
C)225 observations
D)275 observations

Question

Quizplus · Accepted Answer

The formula used for calculating the sample size in work sampling is:
n = (Z^2 * p * q) / d^2
where,
Z = the standard score corresponding to the desired level of confidence (95% in this case) = 1.96
p = the estimated proportion of time the loader is busy = 70% = 0.7
q = 1 - p = 1 - 0.7 = 0.3
d = the desired level of precision (+/- 6% of the actual proportion of time the loader is busy) = 0.06

Plugging in these values, we get:
n = (1.96^2 * 0.7 * 0.3) / 0.06^2
n = 224.37

Rounding up to the nearest whole number, we get 225 observations. Therefore, the best choice is C) 225 observations.

A Work Sampling Study Is Being Conducted on a Loading