Question

Many teens have posted profiles on a social networking website. A sample survey in 2007 asked a random sample of teens with online profiles if they included false information in their profiles. Of 170 younger teens (aged 12 to 14), 117 said “yes.” Of 317 older teens (aged 15 to 17), 152 said “yes.”

C) Do the data give good reason to think there is a difference between the proportions of younger teens and older teens who include false information in their online profiles? Use a significance level of 0.10. Be sure to define the population parameters and state your hypotheses.

Answer 1

Ho:   p1 - p2 =   0          
Ha:   p1 - p2 ╪   0          
                  
sample #1   ----->   experimental          
first sample size,     n1=   170          
number of successes, sample 1 =     x1=   117          
proportion success of sample 1 , p̂1=   x1/n1=   0.6882          
                  
sample #2   ----->   standard          
second sample size,     n2 =    317          
number of successes, sample 2 =     x2 =    152          
proportion success of sample 1 , p̂ 2=   x2/n2 =    0.479          
                  
difference in sample proportions, p̂1 - p̂2 =     0.6882   -   0.4795   =   0.2087
                  
pooled proportion , p =   (x1+x2)/(n1+n2)=   0.5524          
                  
std error ,SE =    =SQRT(p*(1-p)*(1/n1+ 1/n2)=   0.0473          
Z-statistic = (p̂1 - p̂2)/SE = (   0.209   /   0.0473   ) =   4.4159
                        
p-value =        0.0000   [excel formula =2*NORMSDIST(z)]     
decision :    p-value<α,Reject null hypothesis               
                  
Conclusion:   There is enough evidence to say that there is a difference between the proportions of younger teens and older teens who include false information in their online profiles

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