Which of the following statements is true about the standard deviation of $\hat{p}$?
A) It increases as the sample size n increases.
B) It decreases as the sample size n increases.
C) It does not change as the sample size n increases.
D) It changes each time a new sample is drawn.

Question

Quizplus · Accepted Answer

The standard deviation of $\hat{p}$, the sample proportion, decreases as the sample size $n$ increases. This is because the formula for the standard deviation of $\hat{p}$ is $\sqrt{\frac{p(1-p)}{n}}$, where $p$ is the population proportion and $n$ is the sample size. As $n$ increases, the denominator of the fraction under the square root increases, causing the overall value of the standard deviation to decrease.

Which of the Following Statements Is True About the Standard p^\hat{p}p^​

Which of the Following Statements Is True About the Standard $\hat{p}$