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AP Statistics 6.4 Setting Up a Test for a Population Proportion- MCQs - Exam Style Questions

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Question

A candidate running for mayor of a city claims that more than 60 percent of the registered voters of the city favor building a new park. From a survey of 500 registered voters, a newspaper reporter found that 315 favored building a new park.
Which of the following is most appropriate for testing the claim of the candidate running for mayor?
(A) A one-sample z-test for a sample proportion
(B) A one-sample z-test for a population proportion
(C) A one-sample t-test for a population proportion
(D) A one-sample t-test for a population mean
(E) A chi-square test for independence
▶️ Answer/Explanation
We are testing a claim about a single population proportion \(p\) with \(H_0:p=0.60\) vs. \(H_a:p>0.60\).
The data are binary (favor / not favor) and \(n=500\) is large ⇒ use the one-sample z test for a population proportion.
✅ Answer: (B)

Question

According to a certain pet association, \(\,67\%\) of households own a pet. Mazan, a student in a statistics class, wants to investigate whether a greater percentage of households with students from his school own a pet. Mazan will conduct a study by surveying a simple random sample of households with students from his school. Let \(p\) represent the proportion of all households with students from Mazan’s school who own a pet.
Which of the following is an appropriate alternative hypothesis for Mazan’s investigation?
(A) \(H_a:\; p>0.67\)
(B) \(H_a:\; p=0.67\)
(C) \(H_a:\; p<0.67\)
(D) \(H_a:\; \hat p>0.67\)
(E) \(H_a:\; p\neq 0.67\)
▶️ Answer/Explanation
“Greater percentage than \(\,67\%\)” indicates a one-sided alternative about the population parameter \(p\):
\(H_a:\; p>0.67\).
Choices (B) and (E) are not “greater than”; (C) is the wrong direction; (D) incorrectly uses the statistic \(\hat p\) instead of the parameter \(p\).
✅ Answer: (A) \(H_a:\; p>0.67\)
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