Answer to Question #114293 in Statistics and Probability for alivia

Question

In spite of the potential safety hazards, some people would like to have an Internet connection in their car. A preliminary survey of adult Americans has estimated this proportion to be somewhere around 0.20. Use the given preliminary estimate to determine the sample size required to estimate this proportion with a margin of error of 0.02. (Round your answer up to the nearest integer.)

Answer 1

$$ME=z_c\sqrt{{p(1-p)\over n}}$$

The critical value for $\alpha=0.05$ is $z_c=z_{1-\alpha/2}=1.96$

Given $ME=0.02, p=0.2$

$$n\geq{z_c^2p(1-p)\over (ME)^2}$$

$$n\geq{1.96^2(0.2)(1-0.2)\over (0.02)^2}$$

$$n\geq1537$$