Q. 1.4 - The Practice of Statistics for AP

Question

About $75\%$ of young adult Internet users (ages 18 to 29) watch online video. Suppose that a sample survey contacts an SRS of 1000 young adult Internet users and calculates the proportion $\hat{p}$ in this sample who watch online video.

4. If the sample size were 9000 rather than 1000 , how would this change the sampling distribution of $\hat{p}$?

Step-by-Step Solution

Answer

The sampling distribution of $\hat{p}$ is $0.0046$ if the sample size were $9000$ rather than $1000$.

Step 1: Given Information

Population proportion $\left(p\right)=75\%=0.75$

Sample size $\left(n\right)=9000$

Step 2: Explanation

Based on the sample size $9000$ , the mean and standard deviation can be calculated as follows:

$$\begin{gathered} {\mu }_{\hat{p}}=p \\ =0.75 \\ {\sigma }_{\widehat{p}}=\sqrt{\frac{p(1-p)}{n}} \\ =\sqrt{\left(\frac{0.75(1-0.75)}{9000}\right)} \\ =0.0046 \end{gathered}$$