Estimating the Difference between Two Population Proportions — Unit test
Question 5 • CA-Statistics and Probability B
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). Based on this interval, what conclusion should the candidate make about the proportion of likely voters who would vote for her in the upcoming election?
Answer
A
There is a 95% chance that the proportion who would vote for her has increased.
B
The candidate cannot conclude that the proportion of likely voters who would vote for her has increased.
C
It can be stated with 95% confidence that there was no change in the proportion who would vote for her.
D
It can be stated with 95% confidence that there is convincing evidence that the proportion who would vote for her has increased.
Explanation
The interval estimates the change as post-debate minus pre-debate, and it ranges from −0.014 to 0.064. Because the interval includes 0, the data do not provide convincing evidence that the proportion increased; a decrease is also consistent with the interval. The candidate cannot conclude that the proportion of likely voters who would vote for her has increased.
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