AP Statistics Practice Quiz: Concluding a Test for a Population Proportion
Written by AP Content Team, Verified for 2026 AP Exams, Last updated: May 2026
Test your understanding with short quizzes. This quiz has 16 questions to check your progress.
Question 1 of 16
All Questions (16)
A) Reject the null hypothesis.
B) Fail to reject the null hypothesis.
C) Accept the null hypothesis.
D) Reject the alternative hypothesis.
Correct Answer: A
Based on the formal decision rule, if the p-value is less than or equal to the significance level (α), we reject the null hypothesis (H0). Here, 0.03 ≤ 0.05, so we reject H0.
A) There is insufficient evidence to support the alternative hypothesis (Ha).
B) There is sufficient evidence to support the alternative hypothesis (Ha).
C) The null hypothesis (H0) has been proven to be true.
D) The alternative hypothesis (Ha) has been proven to be false.
Correct Answer: B
Rejecting the null hypothesis (H0) means that there is sufficient evidence to support the claim made by the alternative hypothesis (Ha).
A) The null hypothesis is definitely true.
B) There is strong evidence for the null hypothesis.
C) There is insufficient evidence to support the alternative hypothesis.
D) There is sufficient evidence to reject the alternative hypothesis.
Correct Answer: C
Failing to reject the null hypothesis (H0) means that the data does not provide enough evidence to support the alternative hypothesis (Ha). It does not prove that H0 is true.
A) The probability of correctly rejecting the null hypothesis.
B) The probability that the alternative hypothesis is true.
C) The predetermined probability of making a Type I error.
D) The probability of obtaining a test statistic as extreme as the one observed, assuming the null hypothesis is true.
Correct Answer: C
The provided content explicitly states that 'The significance level, alpha, is the predetermined probability of a Type I error.'
A) We fail to reject H0, so there is not enough evidence to conclude that the proportion of residents who support the program is more than 0.60.
B) We reject H0, so there is sufficient evidence to conclude that the proportion of residents who support the program is more than 0.60.
C) We reject H0, which proves that more than 60% of residents support the program.
D) We fail to reject H0, which means the proportion of residents who support the program is exactly 0.60.
Correct Answer: B
Since the p-value (0.02) is less than or equal to alpha (0.05), we reject the null hypothesis (H0). This means there is sufficient evidence for the alternative hypothesis (Ha), which must be stated in context: the proportion of residents who support the program is more than 0.60.
A) It provides evidence for the null hypothesis.
B) It provides evidence for the alternative hypothesis.
C) It proves the null hypothesis is false.
D) It indicates that the significance level was too high.
Correct Answer: B
The provided content states that 'Small p-values provide evidence for the alternative hypothesis.'
A) The test proves that the null hypothesis is true.
B) The test provides convincing evidence that the null hypothesis is true.
C) The test results do not provide convincing evidence for the alternative hypothesis.
D) The test proves that the alternative hypothesis is false.
Correct Answer: C
A large p-value means we do not have convincing evidence for the alternative hypothesis. The content explicitly states that a significance test can never prove the null hypothesis is true.
A) We reject the null hypothesis.
B) We fail to reject the null hypothesis.
C) We have proven the null hypothesis is true.
D) We have sufficient evidence for the alternative hypothesis.
Correct Answer: C
The provided content explicitly states that 'A significance test can never prove the null hypothesis is true.' Therefore, this is never an appropriate conclusion.
A) Reject H₀; there is sufficient evidence that p > 0.5.
B) Reject H₀; there is insufficient evidence that p > 0.5.
C) Fail to reject H₀; there is sufficient evidence that p > 0.5.
D) Fail to reject H₀; there is insufficient evidence that p > 0.5.
Correct Answer: D
The p-value (0.15) is greater than the significance level α (0.10). Therefore, the formal decision is to fail to reject the null hypothesis (H0). This means there is insufficient evidence to support the alternative hypothesis (Ha), which is that p > 0.5.
A) To prove a research question is correct.
B) To provide statistical reasoning to support an answer to a research question.
C) To determine the exact value of the population proportion.
D) To eliminate any possibility of error in a conclusion.
Correct Answer: B
The content states that 'The results of a significance test provide statistical reasoning to support an answer to a research question.' It does not prove anything with certainty.
A) The null hypothesis is true.
B) The alternative hypothesis is true.
C) There is very strong evidence for the null hypothesis.
D) The data do not provide convincing evidence for the alternative hypothesis.
Correct Answer: D
A large p-value (like 0.95) will be greater than any conventional alpha level, leading to a failure to reject H0. The correct interpretation is that there is not convincing evidence for the alternative hypothesis. It does not prove H0 is true.
A) Reject H₀.
B) Fail to reject H₀.
C) The results are inconclusive and the test must be redone.
D) Accept H₀ as true.
Correct Answer: A
The formal decision rule is: if p-value ≤ α, reject H0. Since the p-value (0.01) is equal to alpha (0.01), the condition is met, and the correct decision is to reject the null hypothesis.
A) The p-value was greater than the significance level α.
B) The p-value was less than or equal to the significance level α.
C) The null hypothesis was proven to be false.
D) The significance level α was equal to the p-value.
Correct Answer: B
Concluding there is 'sufficient evidence' for the alternative hypothesis means the null hypothesis was rejected. The condition for rejecting the null hypothesis is that the p-value must be less than or equal to the significance level, α.
A) To prove that the null hypothesis is true or false.
B) To ensure the p-value is smaller than the significance level.
C) To provide a meaningful answer to the original research question.
D) To satisfy the conditions for inference.
Correct Answer: C
The conclusion must be stated in context to provide a clear and understandable answer to the research question that motivated the test. A conclusion like 'reject H0' is not meaningful without the context of what H0 and Ha represent.
A) Both studies provide evidence for the null hypothesis.
B) Study A provides stronger evidence for the alternative hypothesis than Study B.
C) Study B provides stronger evidence for the alternative hypothesis than Study A.
D) Neither study provides evidence for the alternative hypothesis.
Correct Answer: C
Small p-values provide evidence for the alternative hypothesis. The smaller the p-value, the stronger the evidence against the null hypothesis and in favor of the alternative. Since 0.01 < 0.04, Study B provides stronger evidence for the alternative hypothesis.
A) They may have failed to detect a real reduction in defects.
B) They may have concluded the new process is better when it is not, a decision that has a 5% chance of being a Type I error.
C) They may have concluded the new process is better when it is not, a decision that has a 3% chance of being a Type I error.
D) They have proven the new process is better and there is no risk of error.
Correct Answer: B
Rejecting the null hypothesis opens the possibility of a Type I error (rejecting a true H0). The probability of a Type I error is predetermined by the significance level, α. In this case, α = 0.05, so there is a 5% risk of having made a Type I error.