A population of size 1,000 has a proportion of .5. Therefore, the proportion and the standard deviation of the sample proportion for samples of size 100 are _____.
A) 500 and .047
B) 500 and .050
C) .5 and .047
D) .5 and .050

Question

Quizplus · Accepted Answer

The proportion remains .5 regardless of sample size. The standard deviation of the sample proportion is calculated using the formula sqrt[p(1-p)/n], where p is the population proportion and n is the sample size. Substituting the given values (.5 for p and 100 for n) gives sqrt[.5*(1-.5)/100] = sqrt[.25/100] = sqrt[.0025] = .05. However, the correct calculation should result in .05, indicating a mistake in my explanation regarding the standard deviation calculation. The correct standard deviation should indeed be .05, making the correct choice D) .5 and .050, not C as initially stated.

A Population of Size 1,000 Has a Proportion of