(23.38 S-AQ) Teenagers (ages 12 to 17) are much more likely to use instant messa
ID: 3159604 • Letter: #
Question
(23.38 S-AQ) 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 700 out of 991 teens and 497 out of 1220 adults use instant messaging.
Solving the problem step by step, find the following values (±0.0001).
The sample proportion for teenagers: pˆ1 =____ .
The sample proportion for adults: pˆ2 =____ .
The standard error of the statistic pˆ1pˆ2 :____ .
Now, give a 98% confidence interval for the difference between the proportions of teenage and adult Internet users who use instant messaging: ____p1p2___ .
Explanation / Answer
p1hat=700/991=0.71
p2hat=497/1220=0.41
SE(pihat-p2hat)=sqrt[p1hat(1-pihat)/n1+p2hat(1-p2hat)/n2]
=sqrt[(0.71(1-0.71))/991+(0.41(1-0.41))/1220]
=0.02
The 98% c.i=p1hat-p2hat+-Z*SE(p1hat-p2hat)
=(0.71-0.41)+-2.33*0.02
=0.2534 to 0.3466
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