AP Statistics Practice Quiz: Justifying a Claim Based on a Confidence Interval 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

A survey of 1,200 randomly selected adults found that 35% of them use a particular social media platform. A 95% confidence interval for the proportion of all adults who use the platform was calculated to be (0.323, 0.377). Which of the following is the correct interpretation of this confidence interval?

A)There is a 95% probability that the true proportion of all adults who use the platform is between 0.323 and 0.377.B)We are 95% confident that the interval from 0.323 to 0.377 captures the true proportion of all adults who use the platform.C)95% of all adults use the platform between 32.3% and 37.7% of the time.D)We are 95% confident that the sample proportion of adults who use the platform is between 0.323 and 0.377.

All Questions (16)

A) There is a 95% probability that the true proportion of all adults who use the platform is between 0.323 and 0.377.

B) We are 95% confident that the interval from 0.323 to 0.377 captures the true proportion of all adults who use the platform.

C) 95% of all adults use the platform between 32.3% and 37.7% of the time.

D) We are 95% confident that the sample proportion of adults who use the platform is between 0.323 and 0.377.

Correct Answer: B

The correct interpretation of a confidence interval states the confidence level and that the interval captures the population parameter. Option A is incorrect because it implies the population proportion is a random variable; the interval is what's random. Option C misinterprets the meaning of the proportion. Option D is incorrect because the interval is an estimate for the population proportion, not the sample proportion, which is known to be 0.35.

A city's mayor claims that more than 60% of residents support a new recycling initiative. A local newspaper conducts a poll and constructs a 95% confidence interval for the proportion of all residents who support the initiative, which is (0.58, 0.66). Based on this interval, which conclusion is justified?

A) The mayor's claim is correct because the interval contains values greater than 0.60.

B) The mayor's claim is incorrect because the interval contains values less than or equal to 0.60.

C) The interval does not provide convincing evidence for the mayor's claim because 0.60 is a plausible value for the population proportion.

D) The interval provides plausible values for the population proportion, but since some of these values (e.g., 0.59) are not greater than 0.60, the mayor's claim is not supported.

Correct Answer: D

A confidence interval provides a range of plausible values for the population proportion. To justify the claim that the proportion is *more than* 0.60, all plausible values in the interval would need to be greater than 0.60. Since the interval (0.58, 0.66) includes values less than or equal to 0.60, the claim is not supported by this interval.

A statistician is constructing a confidence interval for a population proportion. If the statistician decides to increase the sample size while keeping the confidence level the same, what effect will this have on the width of the confidence interval?

A) The width of the interval will increase.

B) The width of the interval will decrease.

C) The width of the interval will remain unchanged.

D) The effect on the width cannot be determined without knowing the sample proportion.

Correct Answer: B

According to the provided content, the width of a confidence interval tends to decrease as the sample size increases. A larger sample provides more information about the population, leading to a more precise estimate and a narrower interval.

A researcher calculated a 90% confidence interval for the proportion of students who own a laptop. To be more certain about the estimate, the researcher decides to recalculate the interval using a 99% confidence level from the same sample data. How will the 99% confidence interval compare to the 90% confidence interval?

A) The 99% interval will be wider.

B) The 99% interval will be narrower.

C) The 99% interval will be the same width but shifted to the right.

D) The 99% interval will be the same width but shifted to the left.

Correct Answer: A

For a given sample, the width of the confidence interval increases as the confidence level increases. To be more confident that the interval captures the true population proportion, one must include a wider range of plausible values.

A 95% confidence interval for the true proportion of defective widgets produced by a factory is calculated to be (0.08, 0.12). Which of the following statements is a correct conclusion based on this single interval?

A) There is a 95% chance that the true proportion of defective widgets is between 0.08 and 0.12.

B) The method used to create this interval will capture the true proportion of defective widgets 95% of the time in repeated sampling.

C) The true proportion of defective widgets is definitely between 0.08 and 0.12.

D) The probability that this specific interval (0.08, 0.12) contains the true proportion is 0.95.

Correct Answer: B

The confidence level refers to the long-run success rate of the method. For any single calculated interval, the true population proportion either is or is not contained within it. We don't know which is true for this specific interval. Therefore, the confidence is in the method, not in a single outcome.

The margin of error for a 95% confidence interval for a population proportion is found to be 0.03. What is the total width of this confidence interval?

A) 0.015

B) 0.03

C) 0.06

D) 0.95

Correct Answer: C

The width of a confidence interval is exactly twice the margin of error. The interval is constructed by taking the point estimate and adding and subtracting the margin of error. Therefore, the total width is 2 * (margin of error) = 2 * 0.03 = 0.06.

A manufacturer claims that exactly 5% of its light bulbs are defective. A quality control specialist takes a random sample of light bulbs and constructs a 99% confidence interval for the proportion of all defective light bulbs, which is (0.06, 0.09). What is the most appropriate conclusion regarding the manufacturer's claim?

A) The claim is plausible because the interval is close to 0.05.

B) The claim is not plausible because the value 0.05 is not contained within the confidence interval.

C) The claim is plausible because the sample proportion could have been 0.05.

D) The conclusion is uncertain because a 99% confidence level is too high.

Correct Answer: B

A confidence interval provides an interval of plausible values for the population parameter. Since the claimed value of 0.05 is not within the calculated interval of plausible values (0.06, 0.09), the claim is not supported by the sample data.

Which statement best describes the meaning of a 90% confidence level?

A) There is a 90% probability that the population proportion is captured by a single calculated confidence interval.

B) 90% of the sample data will fall within the calculated confidence interval.

C) If we were to take many random samples and construct a confidence interval for each, about 90% of those intervals would capture the true population proportion.

D) We are 90% certain that the sample proportion is equal to the population proportion.

Correct Answer: C

The confidence level describes the long-run capture rate of the method. It means that in repeated sampling, approximately C% (in this case, 90%) of the confidence intervals created will successfully capture the true population proportion.

A political candidate wants to know if they have majority support, which means the proportion of voters who support them is greater than 0.5. They commission a poll which results in a 95% confidence interval for the proportion of all voters who support them of (0.52, 0.58). Which of the following is the strongest conclusion the candidate can make?

A) The candidate cannot conclude they have majority support because 0.5 is not in the interval.

B) The candidate can be confident they have majority support because all plausible values in the interval are greater than 0.5.

C) The candidate cannot draw any conclusion because the sample proportion is not given.

D) The candidate can be 95% certain that the true proportion of their support is exactly the midpoint of the interval, 0.55.

Correct Answer: B

The confidence interval provides a range of plausible values for the population proportion. Since the entire interval (0.52, 0.58) is above 0.5, it provides strong evidence that the true proportion of voters who support the candidate is greater than 0.5. Therefore, the claim of majority support is justified.

A confidence interval for a population proportion is (0.45, 0.55). Which of the following claims would be considered plausible based on this interval?

A) The population proportion is exactly 0.40.

B) The population proportion is at least 0.60.

C) The population proportion is 0.52.

D) The population proportion is less than 0.45.

Correct Answer: C

A confidence interval provides an interval of plausible values for the population proportion. Any value within the interval is considered plausible. Of the options provided, only 0.52 falls within the interval (0.45, 0.55).

Researcher A uses a sample of size n=200 and Researcher B uses a sample of size n=800 from the same population. Both researchers compute a 95% confidence interval for the population proportion. Assuming the sample proportions they obtained were very similar, how would the margin of error for Researcher A's interval likely compare to Researcher B's?

A) Researcher A's margin of error would be smaller.

B) Researcher A's margin of error would be larger.

C) The margins of error would be identical.

D) The relationship cannot be determined without the confidence level.

Correct Answer: B

As sample size increases, the width of the confidence interval tends to decrease. Since the width is twice the margin of error, a larger sample size leads to a smaller margin of error. Researcher A used a smaller sample size (200) than Researcher B (800), so Researcher A's interval will be wider, and their margin of error will be larger.

Which of the following describes the relationship between the confidence level and the margin of error for a confidence interval, assuming the sample size and sample proportion remain constant?

A) As the confidence level increases, the margin of error decreases.

B) As the confidence level increases, the margin of error increases.

C) The confidence level has no effect on the margin of error.

D) The margin of error is always half of the confidence level.

Correct Answer: B

To achieve a higher level of confidence, the interval must be wider to have a better chance of capturing the true population proportion. A wider interval corresponds to a larger margin of error. Therefore, as the confidence level increases, the margin of error also increases.

A pharmaceutical company claims that a new drug is effective for at least 75% of patients. In a clinical trial, a 95% confidence interval for the proportion of patients for whom the drug is effective is found to be (0.72, 0.79). What is the proper conclusion about the company's claim?

A) The claim is supported because the entire interval is above 0.70.

B) The claim is refuted because the interval contains values less than 0.75.

C) The claim is supported because 0.75 is a plausible value within the interval.

D) The claim is refuted because the sample proportion must have been less than 0.75.

Correct Answer: B

The company claims the proportion is at least 0.75 (p ≥ 0.75). The confidence interval (0.72, 0.79) provides a range of plausible values. Since this interval contains values less than 0.75 (e.g., 0.73, 0.74), we cannot conclude that the true proportion is at least 0.75. The data provides plausible scenarios where the claim is false, so the claim is not supported (it is refuted as a certainty).

After calculating a 95% confidence interval, a researcher states, 'This interval (0.61, 0.67) means that the population proportion is a value that falls somewhere between 0.61 and 0.67.' What is the fundamental flaw in this statement?

A) The statement is correct and has no flaws.

B) The statement fails to mention the sample size used to create the interval.

C) The statement implies certainty. A single confidence interval either contains the population proportion or it does not; we are only confident in the method used to generate it.

D) The statement should have referred to the sample proportion, not the population proportion.

Correct Answer: C

A key concept is that any single confidence interval either contains the true population proportion or it does not. The probability or confidence is attached to the method of creating intervals, not to a specific interval that has already been calculated. The statement implies a 100% certainty that the true value is inside, which is incorrect.

An interpretation of a confidence interval for a population proportion must include a reference to which two key elements?

A) The sample size and the margin of error.

B) The sample it represents and the population proportion.

C) The critical value and the standard error.

D) The sample proportion and the population size.

Correct Answer: B

A correct interpretation must be in context. It should clearly identify the population parameter being estimated (the population proportion) and the sample from which the data was gathered to represent that population.

A news organization reported a 95% confidence interval for the proportion of people who approve of the president's performance as (0.42, 0.48). They want to make a claim about whether the president has 'minority approval,' meaning the true proportion is less than 0.50. What conclusion is justified by the interval?

A) The claim of minority approval is not justified because the interval is too wide.

B) The claim of minority approval is not justified because 0.50 is very close to the interval's upper bound.

C) The claim of minority approval is justified because all plausible values in the interval are less than 0.50.

D) No conclusion can be made because the interval does not contain 0.50.

Correct Answer: C

The confidence interval provides a set of plausible values for the true population proportion. Since the entire interval (0.42, 0.48) consists of values less than 0.50, the data provides strong evidence to support the claim that the president has minority approval.