A random sample of $\mathrm { n } = 300$ measurements is drawn from a binomial population with probability of success .26. Give the mean and the standard deviation of the sampling distribution of the sample proportion, $\hat { p }$.
A) .26; .025
B) .26; .011
C) .74; .011
D) .74; .025

Question

Quizplus · Accepted Answer

The mean of the sampling distribution of the sample proportion $\hat{p}$ is equal to the population proportion $p = 0.26$. The standard deviation is calculated as $\sqrt{\frac{p(1-p)}{n}} = \sqrt{\frac{0.26 \times 0.74}{300}} \approx 0.025$.

A Random Sample Of n=300\mathrm { n } = 300n=300 Measurements Is Drawn from a Binomial Population with Probability of Measurements

A Random Sample Of $\mathrm { n } = 300$ Measurements Is Drawn from a Binomial Population with Probability of Measurements