Many teens have posted profiles on a social-networking Web site. A sample survey

Question

Many teens have posted profiles on a social-networking Web site. A sample survey asked random samples of teens with online profiles if they included false information on their profiles. Of 170 younger teens (ages 12 to 14), 117 said "Yes." of 317 older teens (ages 15 to 17), 152 said "Yes." Give a 95% confidence interval for the difference between the proportion of younger and older teens who include false information in their online profiles. Use the plus- four rule. You may use TESTS on your calculator.

Explanation / Answer

According to plus 4 rule

sample proportion for younger teens p'1=(117+2)/(170+4)=0.68

sample proportion for olderteens p'1=(152+2)/(317+4)=0.48

Pooled proportion p'=(117+152+2)/(170+317+4)=0.55

Standard error of difference = sqrt(p'*(1-p')/(n1+n2+4))=sqrt(0.55*(1-0.55)/(170+317+4))=0.02

Margin of error E=1.96*0.02=0.0392

So, 95% cofnidence interval =(p1'-p2')-E ,   (p1'-p2')+E

=(0.68-0.48)-0.0392   (0.68-0.48)+0.0392   

=(0.1608 , 0.2392)

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