AP Statistics Practice Quiz: Carrying Out a Test for the Difference of Two Population Proportions
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) A t-statistic based on the difference in sample means.
B) A chi-square statistic based on a table of observed counts.
C) A z-statistic calculated using the combined (pooled) proportion.
D) An F-statistic based on the ratio of sample variances.
Correct Answer: C
According to the provided content, the test statistic for a difference in proportions is a z-statistic calculated using the combined (pooled) proportion.
A) The alternative hypothesis, that the proportions are different, is true.
B) The null hypothesis, that the proportions are equal, is true.
C) Both sample sizes are greater than 100.
D) The sample proportions are equal to the population proportions.
Correct Answer: B
The content states that interpreting the p-value for a difference of proportions test assumes the null hypothesis (that the proportions are equal) is true. The p-value is the probability of observing a result as extreme or more extreme than the one obtained, given that the null hypothesis is correct.
A) Reject the null hypothesis because the p-value is less than alpha.
B) Fail to reject the null hypothesis because the p-value is less than alpha.
C) Reject the null hypothesis because the p-value is greater than alpha.
D) Fail to reject the null hypothesis because the p-value is greater than alpha.
Correct Answer: A
The provided content specifies that a formal decision compares the p-value to alpha. Since the p-value (0.02) is less than the significance level alpha (0.05), the correct decision is to reject the null hypothesis.
A) The probability that the null hypothesis is true.
B) The probability of observing a difference in sample proportions as or more extreme than the one observed, assuming the population proportions are equal.
C) The probability that the alternative hypothesis is true.
D) The probability of making a Type I error.
Correct Answer: B
The content states that interpreting the p-value assumes the null hypothesis (that the proportions are equal) is true. The p-value itself is the probability of getting the observed result or a more extreme one under this assumption.
A) The study provides convincing statistical evidence that the new medication is effective.
B) The study proves that the medication and the placebo have exactly the same effect.
C) The study did not find convincing statistical evidence that the proportion of patients with side effects is lower for the new medication than for the placebo.
D) The study provides convincing statistical evidence that the new medication is harmful.
Correct Answer: C
Failing to reject the null hypothesis means there is not enough evidence to support the alternative hypothesis. This allows a researcher to justify the claim that there is no statistically significant difference, as stated in the content about justifying a claim based on test results.
A) To get a better estimate of the sample proportions.
B) Because the null hypothesis assumes the two population proportions are equal.
C) To satisfy the large counts condition for inference.
D) To increase the power of the test.
Correct Answer: B
The content specifies that the test statistic uses a combined (pooled) proportion. This is done because the null hypothesis assumes that the two population proportions are the same (p1 = p2). The pooled proportion provides the best estimate of this single, common proportion under the assumption that the null hypothesis is true.
A) prove that the sample proportions are different.
B) calculate the exact difference between the two population proportions.
C) provide statistical reasoning to support or refute a claim about a research question.
D) determine the sample size needed for a future study.
Correct Answer: C
As stated in the provided content, the results of a significance test for a difference of proportions provide statistical reasoning for a research question. This involves assessing the evidence for or against a claim about the populations.
A) Recalculate the test statistic using unpooled proportions.
B) Construct a confidence interval for the difference.
C) Compare the p-value to the pre-determined significance level, alpha.
D) Check if the sample sizes are equal.
Correct Answer: C
The content explicitly states that a formal decision compares the p-value to alpha to reject or fail to reject the null hypothesis. This is the standard procedure after the p-value has been determined.
A) Because 0.1336 > 0.10, we reject the null hypothesis and conclude the proportions are different.
B) Because 0.1336 > 0.10, we fail to reject the null hypothesis. There is not convincing evidence that the proportions of voters supporting the policy in the two states are different.
C) Because -1.50 is negative, we conclude the proportion is lower in the first state.
D) Because 0.1336 is small, we fail to reject the null hypothesis and conclude the proportions are the same.
Correct Answer: B
This question requires integrating multiple concepts. The formal decision rule (content 6) is to compare the p-value (0.1336) to alpha (0.10). Since p > alpha, we fail to reject the null hypothesis. This leads to the justification of the claim (content 3) that there is not enough evidence to conclude the proportions are different.
A) Prove the null hypothesis is false.
B) Justify a claim that there is a difference between the two population proportions.
C) Calculate the exact size of the difference between the two population proportions.
D) Ignore the possibility of a sampling error.
Correct Answer: B
A statistically significant result (which occurs when the p-value is less than alpha) means we reject the null hypothesis. According to the content, the test results are used to justify a claim about the population. In this case, the claim would be in favor of the alternative hypothesis—that a difference exists.
A) The sample means and standard deviations.
B) The degrees of freedom from both samples.
C) The sample proportions and the combined (pooled) proportion.
D) The median values of the two populations.
Correct Answer: C
The content states that the test statistic is a z-statistic calculated using the combined (pooled) proportion. The formula for this z-statistic directly uses the two sample proportions and the calculated pooled proportion.
A) There is a 25% chance that the two population proportions are equal.
B) Assuming the population proportions are equal, there is a 25% chance of observing a difference in sample proportions as large or larger than the one found.
C) There is a 25% chance that the alternative hypothesis is correct.
D) The test is inconclusive and must be redone with a larger sample size.
Correct Answer: B
This question directly tests the interpretation of a p-value. The content specifies that this interpretation assumes the null hypothesis (that the proportions are equal) is true. The p-value is the probability of the observed outcome (or more extreme) under that assumption.
A) They should fail to reject the null hypothesis, as the p-value is very small.
B) They should reject the null hypothesis and conclude there is convincing evidence the new ad is more effective.
C) They should reject the null hypothesis and conclude there is convincing evidence the old ad is more effective.
D) They should accept the null hypothesis because the p-value is not zero.
Correct Answer: B
The p-value of 0.01 is smaller than common alpha levels (like 0.05 or 0.10), leading to the rejection of the null hypothesis. Rejecting the null provides statistical reasoning to support the alternative hypothesis, which is that the new ad's proportion is greater than the old ad's proportion, justifying the claim of higher effectiveness.
A) To find the exact values of the population proportions.
B) To provide a statistical basis for answering a research question about the two populations.
C) To confirm that the samples were collected using a simple random sample method.
D) To eliminate any chance of error in a conclusion about the populations.
Correct Answer: B
The content explicitly states that 'The results of a significance test for a difference of proportions provide statistical reasoning for a research question.' This is the overarching goal of the procedure.
A) The assumption that the proportion of defective items from supplier 1 is actually greater than from supplier 2.
B) The assumption that the samples are perfectly representative of the populations.
C) The assumption that there is no real difference in the proportion of defective items from the two suppliers.
D) The assumption that the z-statistic was calculated correctly.
Correct Answer: C
This is a rephrasing of a core concept. The content states that interpreting the p-value assumes the null hypothesis is true. In this context, the null hypothesis is that the proportions are equal, meaning there is no real difference between the suppliers.
A) Reject H₀, because the p-value is low.
B) Reject H₀, because the p-value is greater than alpha.
C) Fail to reject H₀, because the p-value is greater than alpha.
D) Fail to reject H₀, because alpha is too small.
Correct Answer: C
The content specifies that the formal decision is made by comparing the p-value to alpha. Here, the p-value (0.03) is greater than the significance level alpha (0.01). The correct decision rule is to fail to reject the null hypothesis when the p-value is greater than alpha.