Question 14 • Probability and Statistics with Applications Honors Sem-2-FL-1210300 (2024-2025)
A politician claims that a proposal for a new traffic law is broadly supported by both political parties and that a person from either political party is equally likely to support the proposed legislation. He cites two recent polls that said 70% of a random sample of 550 people from his political party supports the law, and 65% of a random sample of 420 people from the other political party supports the law. The 95 percent confidence interval for the difference in population proportions is (–0.010, 0.110). Based on the interval, is the politician’s claim justified?
Answer
A
The politician’s claim is not justified because the two sample proportions are different.
B
The politician’s claim is justified because the interval contains 0, which indicates no difference in the population proportions.
C
The politician’s claim may be justified because the interval contains 0, which indicates no difference in the population proportions. However, because the interval also contains positive and negative values, it is also plausible that there is a difference in the proportions of party members who support the new traffic law.
D
The politician’s claim is not justified because the interval contains both positive and negative numbers.
Explanation
The 95% confidence interval for the difference in population support proportions runs from −0.010 to 0.110, so it includes 0. That means equal support is plausible, but the interval also includes nonzero differences, so it does not establish that support is equal; a difference in support is plausible too. Thus the politician’s claim may be justified, but the interval does not prove it, as choice C explains.
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