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 2525 subjects randomly selected from an online group involved with ears. 1172 surveys were returned. Construct a 99?% confidence interval for the proportion of returned surveys.

Answer 1

Solution :

Given that,

n = 2525

x = 1172

Point estimate = sample proportion = = x / n = 1172 / 2525 = 0.464

1 - = 0.536

Z_/2 = Z _0.05 = 2.576

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

= 2.576 * (((0.464 * 0.536) / 2525)

= 0.025

A 99% confidence interval for population proportion p is ,

- E < p < + E

0.464 - 0.025 < p < 0.464 + 0.025

0.439 < p < 0.489

99% confidence interval for the proportion of returned surveys is : (0.439, 0.489)