Question

In an ABC News/Washington Post Poll in January 2015, 1,003 adults nationwide answered the following question, 'Obama has proposed providing free tuition to attend community colleges at a cost to the federal government of sixty billion dollars over 10 years. Do you support or oppose this proposal?' 53% supported the proposal with a margin of error of 3.5% at a 95% level of confidence. Which of the following statements is correct about the 95% confidence interval?

A) We are confident that 95% of the 1,003 adults in the sample will support the free community college tuition proposal.
B) We are 95% confident that between 46% and 60% of all adults nationwide will support the free community college tuition proposal.
C) We are 95% confident that between 49.5% and 56.5% of all adults nationwide will support the free community college tuition proposal.
D) We are 95% confident that 53% of the 1,003 adults in the sample will support the free community college tuition proposal.

Answer 1

The correct statement about the 95% confidence interval is that we are 95% confident that between 49.5% and 56.5% of all adults nationwide will support the free community college tuition proposal, which corresponds to option C.

Step-by-step explanation:

The correct statement about the 95% confidence interval for the ABC News/Washington Post Poll is that we are 95% confident that between 49.5% and 56.5% of all adults nationwide will support the free community college tuition proposal. This means letter C is the correct choice. It is important to understand what a confidence interval represents. It does not say that 95% of the 1,003 adults in the sample support the proposal, nor does it guarantee that 53% of the sample supports it. Instead, it gives us a range that we are 95% confident contains the true proportion of all adults who support the proposal.

The confidence interval is calculated by taking the sample percentage (in this case, 53%) and adding and subtracting the margin of error (in this case, 3.5%). Therefore, the lower bound of the confidence interval is 53% - 3.5% = 49.5%, and the upper bound is 53% + 3.5% = 56.5%.