A random sample of $n = 600$ measurements is drawn from a binomial population with probability of success $.08$. Give the mean and the standard deviation of the sampling distribution of the sample proportion, $\hat { p }$.
A) .92; .011
B) .92; .003
C) .08; .011
D) .08; .003

Question

Quizplus · Accepted Answer

The mean of the sampling distribution of the sample proportion $\hat{p}$ is equal to the population proportion $p = 0.08$. The standard deviation is calculated using the formula $\sqrt{\frac{p(1-p)}{n}}$, which gives $\sqrt{\frac{0.08 \times 0.92}{600}} \approx 0.011$.

A Random Sample Of n=600n = 600n=600 Measurements Is Drawn from a Binomial Population with Probability of from a Binomial

A Random Sample Of $n = 600$ Measurements Is Drawn from a Binomial Population with Probability of from a Binomial