Chapter 8: Q 10. (page 507)

Lying online Many teens have posted profiles on sites such as Facebook. A sample survey asked random samples of teens with online profiles if they included false information in their profiles. Of $170$ younger teens (ages role="math" localid="1654194610029" $12 to 14$ ) polled, $117$ said “Yes.” Of $317$ older teens (ages $15 to 17$ ) polled, $152$ said “Yes.” A $95 %$ confidence interval for $pY - pO =$ the true difference in the proportions of younger teens and older teens who include false information in their profile is $0.120$ to $0.297$ .
a. Interpret the confidence interval.
b. Does the confidence interval give convincing evidence of a difference in the true
proportions of younger and older teens who include false information in their profiles?
Explain your answer.

Short Answer

Expert verified

a. There is $95 %$ assurance that correct proportion of young teens include wrong details in their profile is between $0.120 and 0.297$ .

b. There is not enough convincing proof.

Step by step solution

Given Information

It is given that for $95 %$ confidence interval for correct difference in proportion of young teens and older teens that have false information in their respective profiles.

a. To interpret Confidence Interval

From given data, there is $95 %$ confidence that correct proportion of young teens has included wrong information in profiles lies between $0.120$ and $0.297$ high than correct proportion of older teens that has wrong details in their profiles.