Question

in a survey of 980 u.s. teens, 372 said they own smartphones. find standard error of proportion(sep) correct to 2 decimal places 0.05 0.02 0.03 0.04

Explanation:

Step1: Calculate sample proportion

The sample proportion $\hat{p}=\frac{372}{980}\approx0.38$.

Step2: Calculate standard error of proportion

The formula for standard error of proportion is $SEP = \sqrt{\frac{\hat{p}(1 - \hat{p})}{n}}$.
Substitute $\hat{p}=0.38$ and $n = 980$ into the formula:

$$\begin{align*} SEP&=\sqrt{\frac{0.38\times(1 - 0.38)}{980}}\\ &=\sqrt{\frac{0.38\times0.62}{980}}\\ &=\sqrt{\frac{0.2356}{980}}\\ &=\sqrt{0.000240408}\\ &\approx0.0155\approx0.02 \end{align*}$$

Answer:

0.02