A work sampling study requires an acceptable error level of 10% and z = 2 for 95.45% confidence. The adequate sample size is ________ if the sample proportion is thought to be as large as 50%, but ________ if the sample proportion is thought to be about 20%.
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 for sample size n is:
n= (Z^2 * p * q) / E^2
where 
Z = z-score for desired confidence level 
p = estimated proportion of occurrence of event of interest 
q = 1 - p 
E = acceptable error level

For this problem, 
Z = 2 (for 95.45% confidence level), 
E = 0.10 (10% acceptable error level), 
p = 0.5 (when sample proportion is thought to be as large as 50%), 
q = 0.5. 
Plugging these values into the formula, we get:
n = (2^2 * 0.5 * 0.5) / 0.1^2 = 100 
Thus, the adequate sample size is 100 if the sample proportion is thought to be as large as 50%.

When the sample proportion is thought to be about 20%, p = 0.2 and q = 0.8. Plugging these values into the formula, we get:
n = (2^2 * 0.2 * 0.8) / 0.1^2 = 64
Thus, the adequate sample size is 64 when the sample proportion is thought to be about 20%.

Therefore, the best choice is B.

A Work Sampling Study Requires an Acceptable Error Level of 10