Younger people use their cell phones to text more often than older people do. A

Question

Younger people use their cell phones to text more often than older people do. A random sample of 633 teens aged 12 to 17 who use their cell phones to text found that 484 sent more than 10 text messages in a typical day. In a random sample of 1924 adults aged 18 and over who use their cell phones to text, 781 sent more than 10 text messages in a single day.

Give a 96% confidence interval for the difference (teens - adults) between the proportions of cell phone users who send more than 10 texts a day for these two age groups.

The confidence interval (0.001) is from to

Explanation / Answer

Getting p1^ and p2^,          
          
p1^ = x1/n1 =    0.764612954      
p2 = x2/n2 =    0.405925156      
          
Also, the standard error of the difference is          
          
sd = sqrt[ p1 (1 - p1) / n1 + p2 (1 - p2) / n2] =    0.020240217      

For the   96%   confidence level, then  
          
alpha/2 = (1 - confidence level)/2 =    0.02      
z(alpha/2) =    2.053748911      
Margin of error = z(alpha/2)*sd =    0.041568323      
lower bound = p1^ - p2^ - z(alpha/2) * sd =    0.317119475      
upper bound = p1^ - p2^ + z(alpha/2) * sd =    0.400256121      
          
Thus, the confidence interval is          
          
(   0.317119475   ,   0.400256121 ) [ANSWER]

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