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 2357 subjects randomly selected from an online group involved with ears. 1142 surveys were returned. Construct a 95​% confidence interval for the proportion of returned surveys.

Answer 1

Solution :

Given that,

n = 2357

x = 1142

Point estimate = sample proportion = = x / n = 1142 / 2357 = 0.485

1 - = 1 - 0.485 = 0.515

At 95% confidence level

= 1 - 95%

=1 - 0.95 =0.05

/2 = 0.025

Z/2 = Z_{0.025 = 1.960}

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

= 1.96 (((0.485 * 0.515) /2357 )

= 0.020

A 95% confidence interval for population proportion p is ,

± E

= 0.485 ± 0.020

= ( 0.465, 0.505 )