Question

chapter 6 quiz - continuous probability distributions
10 points possible answered: 1/11
question 4
suppose that the efficacy of a certain drug is 0.6. consider the sampling distribution (sample size n = 110) for the proportion of patients cured by this drug.
what is the mean of this distribution?
what is the standard error of this distribution?

next question

Explanation:

Step1: Recall mean formula for sampling distribution of proportion

The mean of the sampling distribution of a proportion $\mu_{\hat{p}}$ is equal to the population - proportion $p$. Given $p = 0.6$, so $\mu_{\hat{p}}=p$.
$\mu_{\hat{p}}=0.6$

Step2: Recall standard - error formula for sampling distribution of proportion

The standard error of the sampling distribution of a proportion $\sigma_{\hat{p}}$ is given by the formula $\sigma_{\hat{p}}=\sqrt{\frac{p(1 - p)}{n}}$, where $p = 0.6$ and $n = 110$.
$\sigma_{\hat{p}}=\sqrt{\frac{0.6\times(1 - 0.6)}{110}}=\sqrt{\frac{0.6\times0.4}{110}}=\sqrt{\frac{0.24}{110}}\approx\sqrt{0.002182}\approx0.0467$

Answer:

Mean: $0.6$
Standard error: $0.0467$