A political candidate feels that she performed particularly well in the most recent debate against her opponent. Her campaign manager polled a random sample of 400 likely voters before the debate and a random sample of 500 likely voters after the debate. The 95% confidence interval for the true difference (post-debate minus pre-debate) in proportions of likely voters who would vote for this candidate was (–0.014, 0.064). What is the correct interpretation of the 95 percent confidence interval? Only 95% of the voters who were polled responded to the question.
The candidate can be 95% confident that the percentage of likely voters who would vote for her increased, since much of the confidence interval is above 0.
The candidate can be 95% confident that the percentage of likely voters who would vote for her did not increase, since the confidence interval contains 0.
We are 95% confident that the interval from –0.014 to 0.064 captures the true change in the proportion of likely voters who would vote for this candidate.