A work sampling study requires an acceptable error level of 10 percent and z = 2 for 95.45 percent confidence. The adequate sample size is __________ if the sample proportion is thought to be as large as 50 percent, but __________ if the sample proportion is thought to be about 20 percent.
A) 50; 20
B) 100; 64
C) 100; 16
D) 20; 50
E) cannot be determined from the information given

Question

Quizplus · Accepted Answer

The formula to calculate the adequate sample size is:

n = (z^2 * p * (1-p)) / e^2

where:

z = z-value for the desired confidence level (z = 2 for 95.45% confidence) 
p = estimated proportion of occurrences (50% for the first part and 20% for the second part) 
e = acceptable error level (10%)

For a proportion of 50%, the worst-case scenario is assumed, so the sample size is the largest:

n = (2^2 * 0.5 * (1-0.5)) / 0.1^2 = 100

For a proportion of 20%, the sample size is smaller:

n = (2^2 * 0.2 * (1-0.2)) / 0.1^2 = 64

A Work Sampling Study Requires an Acceptable Error Level of 10