Question

Two voting districts, C and M, were sampled to investigate voter opinion about tax spending. From a random sample of 100 voters in District C, 22 percent responded yes to the question “Are you in favor of an increase in state spending on the arts?” An independent random sample of 100 voters in District M resulted in 26 percent responding yes to the question. A 95 percent confidence interval for the difference (pc−pm)
was calculated as −0.04±0.12
. Which of the following is the best interpretation of the interval?

We are 95% confident that the majority of all voters in the state favor an increase in state spending for the arts.
A

We are 95% confident that less than half of all voters in the state favor an increase in state spending for the arts.
B

We are 95% confident that the difference in the proportions of all voters in districts C and M who favor an increase in state spending for the arts is between −0.16
and 0.08.
C

We are 95% confident that the difference in the sample proportions of voters in districts C and M who favor an increase in state spending for the arts is between −0.16
and 0.08.
D

We are 95% confident that the proportion of all voters in the state who favor an increase in state spending for the arts is between −0.16
and 0.08.

Answer 1

Answer: We are 95% confident that the difference in the proportions of all voters in districts C and M who favor an increase in state spending for the arts is between −0.16 and 0.08.

>> We sampled for the proportion of voters in districts C and M.

The lower limit for the confidence interval = - 0.04 - 0.12 = - 0.16

Th upper limit for the confidence interval = -0.04 + 0.12 = 0.08

We calculate the confidence interval for the difference in population proportions of all voters in districts C and M.

Hence, the interpretation is: we are 95% confident that the difference in the proportions of all voters in districts C and M who favor an increase in state spending for the arts is between −0.16 and 0.08.