Question

A random sample of 83 residents of a certain town were asked whether they approve of a proposal to improve the town’s aging bridges. The 95 percent confidence interval to estimate the proportion of all residents of the town who approve of the proposal was calculated to be (0.361,0.579).

Which of the following is a correct interpretation of the interval?

Answer 1

We are 95 percent confident that the proportion of all residents in the town who favor the proposal is between 0.361 and 0.579.

Explanation:

The question states that there is a 95% confidence interval, so the answer must start off by saying "we are 95 percent confident". It also states that the proportion of all residents of the town who approve of the proposal was calculated to be (0.361,0.579), so this must be exactly quoted in the answer choice as well.

Answer 2

We are 95% sure that the true proportion of all residents of the town who approve of the proposal is between 0.361 and 0.579.

Explanation:

x% confidence interval of a sample between a and b.

What is the interpretation?

The interpretation is that we are x% sure that the true population proportion is between a and b.

In this problem:

The 95 percent confidence interval to estimate the proportion of all residents of the town who approve of the proposal was calculated to be (0.361,0.579).

Interpretation:

We are 95% sure that the true proportion of all residents of the town who approve of the proposal is between 0.361 and 0.579.