Question

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" $12\mathrm{to}14$) polled, $117$said “Yes.” Of $317$older teens (ages $15\mathrm{to}17$) polled, $152$said “Yes.” A $95\%$confidence interval for $\mathrm{pY}-\mathrm{pO}=$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

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

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.

To Explain the convincing evidence of a difference in the true proportion of younger and older teens of confidence interval

Confidence Interval does not contain zero, it is likely that there is not any difference in correct proportion of young and older teens.

Hence, there is enough of the convincing proof in true proportion of young and old teens that has wrong data in their profile.