What are the mean and the standard deviation of the sampling distribution of $\hat { p }$
?
A)14 and 250
B)14 and .1204
C)35 and 5.486
D)14 and .0219
E)35 and 30.1

Question

Quizplus · Accepted Answer

The mean of the sampling distribution of $\hat { p }$ is equal to the population proportion, and the standard deviation of the sampling distribution of $\hat { p }$ is calculated using the formula $\sqrt{\frac{p(1-p)}{n}}$, where $p$ is the population proportion and $n$ is the sample size. Without specific values for $p$ and $n$, we can't calculate the exact numbers, but the correct answer must pair a mean (which is a proportion and thus should be between 0 and 1) with a standard deviation that follows the formula's structure. Among the options, only D pairs a plausible mean (if we consider it as a proportion, not an absolute number, which seems to be a typo or misunderstanding in the options) with a standard deviation that fits the expected structure for a proportion's standard deviation.

What Are the Mean and the Standard Deviation of the Sampling