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 2584 subjects randomly selected from an online group involved with ears.926 surveys were returned. Construct a 95% confidence interval for the proportion of returned surveys.

Find the best point estimate of the population proportion p.

Identify the value of the margin of error E.

Construct the confidence interval.

Answer 1

Solution :

Given that,

n = 2584

x = 926

Point estimate = sample proportion = = x / n = 926 / 3584 = 0.358

1 - = 1 - 0.358 = 0.642

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z_/2 = Z_0.025 = 1.96

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

= 1.96 * (((0.358 * 0.642) / 2584)

= 0.018

A 95% confidence interval for population proportion p is ,

- E < p < + E

0.358 - 0.018 < p < 0.358 + 0.018

0.340 < p < 0.376

The 95% confidence interval for the population proportion p is : (0.340 , 0.376)