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)200;80

Question

Quizplus · Accepted Answer

The formula for calculating the required sample size for a work sampling study is:

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

where 
z = critical value from the standard normal distribution for the desired level of confidence 
p = estimated proportion of time the activity being observed is occurring 
E = acceptable error level

For the first part of the question, where the sample proportion is thought to be as large as 50 percent, we can use p = 0.5. Thus,

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

For the second part of the question, where the sample proportion is thought to be about 20 percent, we can use p = 0.2. Thus,

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

Therefore, the best choice is B, where the adequate sample size is 100 if the sample proportion is thought to be as large as 50 percent, but 64 if the sample proportion is thought to be about 20 percent.

A Work Sampling Study Requires an Acceptable Error Level of 10