Question

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%

Answer 1

Answer: 10% and 70%

Explanation:

Given : The percentage of people reported that they recycle on a regular basis :
`\hat{p} =69\%`

Margin of error :
`E= 4.5\%`

Confidence interval for percentage :

`\hat{p} \pm\ E\\\\=69\%\pm4.5\%\\\\=(69\%-4.5\%\ , 69\%+4.5\%)=(64.5\%\ ,\ 73.5\%)`

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%.