Teenagers ages 12 to 17 are much more likely to use instant

Teenagers (ages 12 to 17) are much more likely to use instant messaging online than are adults (ages 18 and older). How much more likely? A random sample of Internet users found that 761 out of 942 teens and 468 out of 1228 adults use instant messaging.

Solving the problem step by step, find the following values (±0.0001).

Solution

Formulating the hypotheses          
Ho: p1^ - p2^   <=   0  
Ha: p1^ - p2^   >   0  
Here, we see that pdo =    0   , the hypothesized population proportion difference.  
          
Getting p1^ and p2^,          
          
p1^ = x1/n1 =    0.807855626 [answer]      
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p2^ = x2/n2 =    0.381107492 [answer]
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Also, the standard error of the difference is          
          
sd = sqrt[ p1 (1 - p1) / n1 + p2 (1 - p2) / n2] =    0.018890591 [answer]

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Lower Bound = (p1^-p2^) - z(alpha/2) * se              
Upper Bound = (p1^-p2^) + z(alpha/2) * se              
              
where              
              
alpha/2 = (1 - confidence level)/2 =    0.025          
              
Thus,              
(p1^-p2^) = sample mean =    0.426748134  
z(alpha/2) = critical z for the confidence interval =    1.959963985          
se = standard error =    0.018890591          
              
              
Thus,              
              
Lower bound =    0.389723256          
Upper bound =    0.463773012          
              
Thus, the confidence interval is              
              
(   0.389723256   ,   0.463773012   ) [answer]