In a recent study, it was reported that the proportion of employees who miss work on Fridays is 0.15, and that the standard deviation of the sample proportion is .However, the report did not indicate the sample size n.What was the sample size, assuming the Central Limit Theorem holds in this case?
A) 26
B) 58
C) 102
D) 204

Question

In a recent study, it was reported that the proportion of employees who miss work on Fridays is 0.15, and that the standard deviation of the sample proportion is  .However, the report did not indicate the sample size n.What was the sample size, assuming the Central Limit Theorem holds in this case?
A) 26 
B) 58 
C) 102 
D) 204

Quizplus · Accepted Answer

The Central Limit Theorem applies when the sample size is large enough, typically n≥30. We can use the formula for the standard deviation of the sample proportion, which is:
σp=√(p(1-p)/n)
where p is the true proportion and n is the sample size. Since we are given the standard deviation of the sample proportion σp=0.11, we can use this to solve for n:
0.11=√(0.15(1-0.15)/n)
0.0111^2=0.15(1-0.15)/n
n=0.15(1-0.15)/(0.0111^2)
n≈203.95
Since n must be a whole number, the nearest value is 204. Therefore, the sample size is 204, and the answer is D.

In a Recent Study, It Was Reported That the Proportion