Question

Use the sample data and confidence level given below to complete parts​ (a) through​ (d). In a study of cell phone use and brain hemispheric​ dominance, an Internet survey was​ e-mailed to 2434 subjects randomly selected from an online group involved with ears. 1055 surveys were returned. Construct a 99​% confidence interval for the proportion of returned surveys.

​a) Find the best point estimate of the population proportion p.

Answer 1

Solution :

Given that,

Point estimate () = x / n = 1055 / 2434 = 0.4334

1 - = 0.5666

Z/2 = 2.576

Margin of error = E = Z / 2 * (( * (1 - )) / n)

= 2.576 * [(0.4334 * 0.5666) / 2434]

= 0.026

A 99% confidence interval for population proportion p is ,

- E < p < + E

0.4334 - 0.026 < p < 0.4334 + 0.026

0.4074 < p < 0.4564

(0.4074, 0.4564)