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 2346 subjects randomly selected from an online group involved with ears. 1070 surveys were returned. Construct a 90​% confidence interval for the proportion of returned surveys. LOADING... Click the icon to view a table of z scores. ​a) Find the best point estimate of the population proportion p.

Answer 1

Solution :

Given that,

n = 2346

x = 1070

Point estimate = sample proportion = = x / n = 1070/2346=0.456

1 -   = 1- 0.456 =0.544

At 90% confidence level

= 1 - 90%  

= 1 - 0.90 =0.10

/2 = 0.05

Z/2 = Z0.05 = 1.645 ( Using z table )

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

= 1.645 *((0.456*0.544) /2346 )

= 0.017

A 90% confidence interval for proportion is ,

- E < p < + E

0.456-0.017 < p < 0.456+0.017

0.439< p < 0.473

The 90% confidence interval for the proportion p is : (0.439 ,  0.473)