Question

A major insurance company looked at teen cell phone use, specifically while driving. Eighty-two percent were using phones in the sample of fifty drivers.

a. Construct the 95% confidence interval for the proportion of all teenagers that have used cell phones while driving. (Round answers to 2 decimal places.)

b. What is the margin of error with 95% confidence? (Round answer to 2 decimal places.)

Answer 1

Solution :

Given that,

n = 50

Point estimate = sample proportion = =0.82

1 - = 1 - 0.82=0.18

At 95% confidence level

= 1 - 95%  

= 1 - 0.95 =0.05

/2 = 0.025

Z/2 = Z_{0.025 = 1.96}

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

= 1.96 (((0.82*0.18) /50 )

= 0.11

A 95% confidence interval for population proportion p is ,

- E < p < + E

0.82-0.11 < p < 0.82+ 0.11

0.71< p < 0.93

(0.71 , 0.93)