The Berkman Center Study referenced in Example $8.13$talked to teens in smaller focus groups but also interviewed additional teens over the phone. When the study was complete,$588$teens had answered the question about their Facebook friends with $159$saying that they have more than $500$friends. Use the“plus-four”methodtofinda$90$% confidence interval for the true proportion of teens that would report having more than $500$Facebook friends based on this larger sample. Compare the results to those in Example $8.13$.

n= $588$

The number of teens having friends more than $500$is $159$

The sample of $588$teens had answered the question about Facebook, that is, n=$588$

The number of teens having friends more than $500$is $159$

By the "plus-four" rule, the new values are shared below,

x =$159+2$

=$161$

n =$588+4$

$=592$

Now compute the confidence interval using TI-$83$ calculator using the steps given below,

Step 1: press STAT and use the arrow(?) to TESTS

Step 2: Now press the arrow $(\downarrow )$to A:1 Propzint and press enter.

Step 3: Now press the arrow (?) and enter the inputs as shown below.

Step 4: Then press the arrow (?) to calculator and press enter. The output is given below.

The $90$% confidence interval for the true proportion of teens having friends more than $500$is [$0.241880,0.30204$]