A random sample of $\mathrm { n } = 400$ measurements is drawn from a binomial population with probability of success .21. Give the mean and the standard deviation of the sampling distribution of the sample proportion, $\hat { p }$.
A) $.21 ; .008$
B) .79; .02
C) .79; .008
D) .21; .02

Question

Quizplus · Accepted Answer

The mean of the sampling distribution of the sample proportion $\hat{p}$ is equal to the population proportion $p = 0.21$. The standard deviation is calculated using the formula $\sqrt{\frac{p(1-p)}{n}}$, which gives $\sqrt{\frac{0.21 \times 0.79}{400}} = 0.02$.

A Random Sample Of n=400\mathrm { n } = 400n=400 Measurements Is Drawn from a Binomial Population with Probability of Measurements

A Random Sample Of $\mathrm { n } = 400$ Measurements Is Drawn from a Binomial Population with Probability of Measurements