AP Statistics Practice Quiz: Interpreting p-Values
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) The probability of obtaining a test statistic as or more extreme than the observed one, assuming the null hypothesis is true.
B) The probability that the null hypothesis is true given the observed test statistic.
C) The probability that the alternative hypothesis is true.
D) The value of the standardized test statistic itself.
Correct Answer: A
This is the formal definition provided in the content. A p-value is a conditional probability, calculated under the assumption that the null hypothesis is the true state of the world.
A) The alternative hypothesis is true.
B) The sample size is sufficiently large.
C) The null hypothesis is true.
D) The sample statistic is equal to the population parameter.
Correct Answer: C
The content explicitly states that interpreting a p-value assumes the null hypothesis is true. The p-value calculates the probability of the observed data *given* that the null is true.
A) There is a 4% chance that the null hypothesis is true.
B) Assuming the null hypothesis is true, there is a 4% chance of observing a test statistic as or more extreme than the one calculated.
C) There is a 4% chance that the alternative hypothesis is false.
D) The sample proportion is only 4% different from the true population proportion.
Correct Answer: B
The p-value is the probability of getting the observed result (or a more extreme one) purely by random chance, under the condition that the null hypothesis is true.
A) The standard deviation of the sampling distribution.
B) The probability of observing the sample statistic.
C) The difference between the observed evidence and the value assumed by the null hypothesis.
D) The p-value of the significance test.
Correct Answer: C
The numerator measures how far the observed sample statistic deviates from the parameter value specified in the null hypothesis.
A) The distribution of the sample data.
B) The distribution of the population.
C) The null distribution, which can be a theoretical z-distribution.
D) The distribution of all possible p-values.
Correct Answer: C
The content states that the null distribution of the test statistic is a theoretical (e.g., z) distribution, and the p-value is a proportion of this distribution.
A) The p-value is actually the chance that the alternative hypothesis is correct.
B) The p-value is calculated assuming the null hypothesis is true; it cannot be the probability of the null hypothesis being true.
C) This interpretation is only correct if the p-value is greater than 0.05.
D) The p-value measures the size of the effect, not the probability of a hypothesis.
Correct Answer: B
The p-value is a conditional probability based on the *assumption* that the null is true. It measures the strength of evidence against the null, not the probability of the null itself.
A) Closer to the mean of the null distribution.
B) As far from the null value as the observed statistic, or even farther, in the direction of the alternative hypothesis.
C) Exactly equal to the observed sample statistic.
D) Associated with a larger standard deviation.
Correct Answer: B
"Extreme" means far from what we would expect if the null hypothesis were true. The p-value accumulates the probability in the tail(s) of the null distribution, starting from the observed test statistic.
A) As the peak of the null distribution curve.
B) As the total area under the null distribution curve.
C) As the proportion of the area in the tail(s) of the null distribution that is as or more extreme than the observed test statistic.
D) As the x-axis value corresponding to the sample statistic.
Correct Answer: C
The content specifies that the p-value is the proportion of the null distribution that is as or more extreme than the observed test statistic, which corresponds to the area in the tail(s) of the distribution.
A) It is the value of the proportion calculated from the sample data.
B) It is the hypothesized value of the population proportion under the null hypothesis, used as a point of reference.
C) It is the standard deviation of the sample statistic.
D) It is the final p-value of the test.
Correct Answer: B
The "null value" is the specific value of the parameter (in this case, the population proportion) that the null hypothesis claims to be true. The test statistic measures the distance of the sample statistic from this value.
A) Getting a z-statistic of exactly -2.0, assuming p = 0.50.
B) Getting a z-statistic of -2.0 or greater, assuming p = 0.50.
C) Getting a z-statistic of -2.0 or less, assuming p = 0.50.
D) Getting a z-statistic of 2.0 or greater, assuming p = 0.50.
Correct Answer: C
Since the alternative hypothesis is left-tailed (p < 0.50), "more extreme" means further to the left on the number line. Therefore, the p-value is the probability of obtaining a test statistic of -2.0 or any value even smaller (more negative), assuming the null hypothesis (p = 0.50) is true.
A) A chi-squared statistic
B) A t-statistic
C) A z-statistic
D) An F-statistic
Correct Answer: C
The provided content explicitly states that the test statistic for a population proportion is a specific z-statistic formula, which is a type of standardized test statistic.
A) There is a 2% chance that a majority of people prefer the new product.
B) There is a 2% chance that the observed sample proportion occurred by random chance.
C) If the true proportion of people who prefer the new product was exactly 0.5, there would be a 2% probability of getting a sample proportion as high as or higher than the one observed.
D) The probability that the true proportion is 0.5 is only 2%.
Correct Answer: C
This interpretation correctly includes all three key components: the assumption that the null hypothesis is true (true proportion is 0.5), the probability (2%), and the description of the event (getting a sample proportion as or more extreme than observed).
A) To determine the exact value of the population proportion.
B) To measure how likely the observed test statistic is, assuming the null hypothesis is true.
C) To prove that the null hypothesis is false.
D) To calculate the standard deviation of the statistic.
Correct Answer: B
The p-value quantifies the "surprisingness" of the data. It is the probability of seeing a result as extreme as the one observed, under the assumption that the null hypothesis is correct. A small probability suggests the data is surprising under the null.
A) Assuming the null hypothesis is true, the observed test statistic is not particularly unusual.
B) The probability of obtaining a test statistic as or more extreme than the observed one is 0.28, if the null hypothesis is true.
C) There is a 28% chance that the null hypothesis is true.
D) The observed result provides little evidence against the null hypothesis.
Correct Answer: C
The p-value is not the probability that the null hypothesis is true. This is a common and critical misinterpretation. The p-value is calculated *assuming* the null is true.
A) To measure the difference between the sample and the null value.
B) To convert the difference in the numerator into a standardized number of standard deviations.
C) To calculate the p-value directly.
D) To represent the value of the population parameter.
Correct Answer: B
The denominator is the standard deviation of the sampling distribution of the statistic. Dividing by it standardizes the difference found in the numerator, allowing us to see how many standard deviations away from the null value our sample statistic is.
A) The true population proportion is very likely to be 0.7.
B) The sample proportion of 0.68 is a very rare outcome.
C) There is a 45% chance that the null hypothesis is correct.
D) If the true population proportion were 0.7, an outcome as or more extreme than a sample proportion of 0.68 would occur in about 45% of samples.
Correct Answer: D
A large p-value like 0.45 means that the observed data (a sample proportion of 0.68) is not surprising or unusual if the null hypothesis (p=0.7) were true. Option D correctly frames this as the probability of the observed outcome (or more extreme) under the condition of the null hypothesis.