the proportion of all high school students who watch national news is $p = 0.47$. a random sample of 50 high…

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 $hat{p}$?\n$mu_{hat{p}}=p = 0.47$\n$mu_{hat{p}}=np = 50(0.47)=23.5$\n$mu_{hat{p}}=1 - p=1 - 0.47 = 0.53$\n$mu_{hat{p}}=n(1 - p)=50(1 - 0.47)=26.5$

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 $hat{p}$?\n$mu_{hat{p}}=p = 0.47$\n$mu_{hat{p}}=np = 50(0.47)=23.5$\n$mu_{hat{p}}=1 - p=1 - 0.47 = 0.53$\n$mu_{hat{p}}=n(1 - p)=50(1 - 0.47)=26.5$

Answer

Explanation:

Step1: Recall sampling - distribution property

The mean of the sampling distribution of the sample - proportion $\hat{p}$ is equal to the population proportion $p$ when sampling is done randomly.

Step2: Identify given values

We are given that $p = 0.47$ and $n=50$. According to the formula $\mu_{\hat{p}}=p$.

Answer:

$\mu_{\hat{p}}=p = 0.47$ (First option)