Q.1.2. - The Practice of Statistics for AP

Question

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

Find the standard deviation of the sampling distribution of $\overbrace{p}$.check that the $10\%$condition is met.

Step-by-Step Solution

Answer

The standard deviation is $0.0137$

Step-1 Given Information

Given in the question that 

population proportion $\left(P\right)=75\%=0.75$

Sample size$\left(n\right)=1000$we have to find the standard deviation.

Step-2 Explanation

The standard deviation of the sampling distribution $\overbrace{p}$ is:

$$\begin{gathered} {\sigma }_p=\sqrt{\frac{p(1-p)}{n}} \\ =\sqrt{\frac{0.75(1-0.75)}{1000}} \\ =0.0137 \end{gathered}$$