A population of size 1,000 has a proportion of 0.5. Therefore, the proportion and the standard deviation of the sample proportion for samples of size 100 are
A) 500 and 0.047.
B) 500 and 0.050.
C) 0.5 and 0.047.
D) 0.5 and 0.050.

Question

Quizplus · Accepted Answer

The proportion remains 0.5. The standard deviation of the sample proportion is calculated using the formula $\sqrt{\frac{p(1-p)}{n}}$, where $p = 0.5$ and $n = 100$. This gives $\sqrt{\frac{0.5(1-0.5)}{100}} = \sqrt{\frac{0.25}{100}} = \sqrt{0.0025} = 0.05$. However, there seems to be a mistake in my calculation as the correct standard deviation should be 0.05, aligning with option D, not C. My explanation incorrectly supports C due to a miscalculation. The correct answer, based on the correct calculation, should be D, not C.

A Population of Size 1,000 Has a Proportion of 0