Q:

An activist asks people in his apartment complex about their recycling behavior. Sixty-nine percent of the people reported that they recycle on a regular basis, and the margin of error was 4.5%. Which of the following intervals does not include 95% confidence interval? O 10% and 70% 30% and 75% 60% and 80% O 63% and 74%

Accepted Solution

A:
Answer:   10% and 70%Step-by-step explanation:Given : The percentage of  people reported that they recycle on a regular basis : [tex]\hat{p} =69\%[/tex]Margin of error :[tex]E= 4.5\%[/tex]Confidence interval for percentage :[tex]\hat{p} \pm\ E\\\\=69\%\pm4.5\%\\\\=(69\%-4.5\%\ , 69\%+4.5\%)=(64.5\%\ ,\ 73.5\%)[/tex]Let's check the given options : 10% and 70%  , it do not contains the above interval as upper bound of this  interval (70%) is lower than the upper bound of confidence interval (73.5%) 30% and 75% , it contains confidence interval( 64.5% , 73.5% ).60% and 80%, it contains confidence interval( 64.5% , 73.5% ).63% and 74% , it contains confidence interval( 64.5% , 73.5% ).Hence, the correct answer is 10% and 70%.