In a study of cell phone use and brain hemispheric​ dominance, an Internet survey was​ e-mailed to 2617 subjects randomly selected from an online group involved with ears. surveys were returned. Construct a 99% confidence interval for the proportion of returned surveys.

Answer:

Given Data :

Favorable cases $(x)=932$

Sample size $(n)=2,617$

Confidence interval level $=99$

Solution:

The sample proportion $(\hat{p})=\frac{x}{n}=\frac{932}{\mathrm{2,617}}=0.35613$

The significance level $(\alpha )=1–0.99=0.01$

The confidence interval :

$$CI=\hat{p}\pm z_c\times \sqrt{\frac{\hat{p}(1–\hat{p})}{n}}$$ $$=0.3561\pm 2.576\times \sqrt{\frac{0.3561(1–0.3561)}{\mathrm{2,617}}}$$ $$=(0.332,0.380)$$