Question

the proportion of all high school students who watch national news is $p = 0.47$. a random sample of 50 high school students is selected. which of the following is the mean of the sampling distribution of $hat{p}$?
$mu_{hat{p}}=p = 0.47$
$mu_{hat{p}}=np = 50(0.47)=23.5$
$mu_{hat{p}}=1 - p = 1 - 0.47 = 0.53$
$mu_{hat{p}}=n(1 - p)=50(1 - 0.47)=26.5$

Explanation:

Step1: Recall the property of the sampling distribution of the sample proportion

The mean of the sampling distribution of the sample proportion \(\hat{p}\), denoted as \(\mu_{\hat{p}}\), is equal to the population proportion \(p\).

Answer:

\(\mu_{\hat{p}}=p = 0.47\) (the first option)