Question

A phone survey has a margin error of +/– 4%. What is the range of number of people who will vote for the other candidate if 87 of 114 people said they would vote for the other person and there are 9918 people in the district?

Answer 1

You should divide 87 by 114 for the precent of people. 76% with an margin either way is between 80% and 72%.

Answer 2

`(1952, 2745)`

Explanation:

Given that a phone survey has a margin error of +/– 4%.

Proportion favouring our candidate =
`(87)/(114) =0.7632`

Proportion not favouring our candidate =
`1-0.7632 = 0.2368`

Margin of error = 4%

i.e. confidence interval = (0.2368-0.04, 0.2368+0.04)

=
`(0.1968, 0.2768)`

Total no of people in the district = 9918

Hence range for these who vote for other candidate

=
`(0.1968*9918, 0.2768*9918)\\=(1952, 2745)`