Question 9 • Probability and Statistics with Applications Honors Sem-2-FL-1210300 (2024-2025)
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?
Answer
A
Only 95% of the voters who were polled responded to the question.
B
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.
C
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.
D
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.
Explanation
A 95% confidence interval for the difference in proportions means we are 95% confident that the interval from −0.014 to 0.064 contains the true post-debate minus pre-debate change in the proportion of likely voters who would vote for the candidate. Because the interval includes 0, the data do not establish that support increased or decreased. Choice D gives the correct interpretation; choice C incorrectly treats including 0 as proof that support did not increase.
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