Free AP® Statistics Practice Test (2026)

Question 1

The household incomes in a town have a distribution that is strongly skewed to the right. Which is most likely true?

Accepted Answer

The mean income is greater than the median income.

Answer

The median income is greater than the mean income.

Answer

The mean and median incomes are equal.

Answer

The standard deviation is smaller than the interquartile range.

Question 2

In a group of 200 students, 80 are juniors and 120 are seniors. Of the juniors, 30 drive to school; of the seniors, 66 drive. A student who drives is chosen at random. What is the probability that the student is a senior?

Accepted Answer

About 0.69

Answer

About 0.83

Answer

0.55

Answer

0.33

Question 3

In a random sample of 400 adults, 60% say they prefer to read news online. What is the margin of error for a 95% confidence interval for the population proportion?

Accepted Answer

About 0.048

Answer

About 0.096

Answer

About 0.063

Answer

About 0.024

Question 4

A least-squares regression line predicts exam score from hours studied: predicted score = 12 + 3.5(hours). Which is the correct interpretation of the slope?

Accepted Answer

For each additional hour studied, the predicted exam score increases by 3.5 points.

Answer

For each additional hour studied, every student’s score increases by exactly 3.5 points.

Answer

A student who studies 0 hours is predicted to score 3.5 points.

Answer

About 3.5% of the variation in scores is explained by hours studied.

Question 5

A school picks a sample by randomly selecting 20 students from each of its four grade levels. What kind of sample is this?

Accepted Answer

A stratified random sample

Answer

A cluster sample

Answer

A systematic random sample

Answer

A simple random sample

Question 6

A population has a standard deviation of 12. What is the standard deviation of the sampling distribution of the sample mean for random samples of size 36?

Accepted Answer

2

Answer

0.33

Answer

6

Answer

12

Question 7

Events A and B are independent, with P(A) = 0.4 and P(B) = 0.5. What is P(A or B)?

Accepted Answer

0.7

Answer

0.2

Answer

0.5

Answer

0.9

Question 8

For a set of data, Q1 = 20 and Q3 = 32. Using the 1.5 × IQR rule, which of these values would be an outlier?

Accepted Answer

53

Answer

44

Answer

47

Answer

49

Question 9

A test of H₀: p = 0.50 against Hₐ: p > 0.50 gives a p-value of 0.03. Which is the correct interpretation of the p-value?

Accepted Answer

If the true proportion were 0.50, there would be a 0.03 probability of getting a sample result at least as extreme as the one observed.

Answer

There is a 0.03 probability that the null hypothesis is true.

Answer

There is a 0.97 probability that the alternative hypothesis is true.

Answer

If the alternative were true, 3% of samples would give this result.

Question 10

Using the regression line predicted score = 12 + 3.5(hours), what is the residual for a student who studied 10 hours and scored 50?

Accepted Answer

3

Answer

−3

Answer

47

Answer

50

Question 11

A news website asks readers to vote online on whether the city should build a new stadium, and 78% of the 5,000 responses say no. Why is this result likely biased?

Accepted Answer

People who choose to respond often have strong opinions that differ from those of the whole population.

Answer

The sample is too small to represent a city.

Answer

The question wording is leading.

Answer

Readers were assigned to vote at random.

Question 12

Researchers record each of 25 volunteers’ reaction times once without caffeine and once with caffeine. Which procedure is appropriate for testing whether caffeine changes mean reaction time?

Accepted Answer

A paired t-test on the differences in reaction time

Answer

A two-sample t-test comparing the two sets of times

Answer

A chi-square test of independence

Answer

A two-sample z-test for proportions

Question 13

A fair coin is tossed 4 times. What is the probability of getting exactly 2 heads?

Accepted Answer

0.375

Answer

0.625

Answer

0.5

Answer

0.25

Question 14

A chi-square test of independence is done on a two-way table with 3 rows and 4 columns. How many degrees of freedom does the test have?

Accepted Answer

6

Answer

12

Answer

11

Answer

7

Question 15

A study randomly assigns 100 volunteers to take either a new sleep aid or a placebo, and the sleep aid group sleeps much longer on average. Which conclusion is justified?

Accepted Answer

The sleep aid caused the longer sleep for volunteers like these, but the results may not apply to all adults.

Answer

The sleep aid causes longer sleep for all adults.

Answer

The study shows only an association, because volunteers were used.

Answer

No conclusion is possible, because there was no random sample.

Question 16

The correlation between two variables is r = −0.8. Which statement about r² is correct?

Accepted Answer

About 64% of the variation in the response variable is accounted for by the linear relationship with the explanatory variable.

Answer

About 80% of the variation in the response variable is accounted for by the linear relationship.

Answer

About 64% of the predictions made with the line will be exactly correct.

Answer

Because r is negative, the line explains −64% of the variation.

Question 17

A game pays $10 with probability 0.1, $2 with probability 0.3, and nothing otherwise. What is the expected payout of one play?

Accepted Answer

$1.60

Answer

$12.00

Answer

$6.00

Answer

$4.00

Question 18

A 95% confidence interval for the mean commute time of workers in a city is 22.4 to 27.6 minutes. Which is the correct interpretation?

Accepted Answer

We are 95% confident that the mean commute time of all workers in the city is between 22.4 and 27.6 minutes.

Answer

95% of workers in the city commute between 22.4 and 27.6 minutes.

Answer

There is a 95% probability that the sample mean is between 22.4 and 27.6 minutes.

Answer

95% of all sample means will fall between 22.4 and 27.6 minutes.

Question 19

In a random sample of 50 people, 6 say they own an electric car. Which condition for a one-sample z-interval for a proportion is not met?

Accepted Answer

The large counts condition, because there are fewer than 10 successes

Answer

The random condition, because the sample is too small

Answer

The 10% condition, because 50 is more than 10% of the population

Answer

The normality of the population, because ownership is not normal

Question 20

On a test with a mean of 70 and a standard deviation of 8, what is the z-score of a student who scored 82?

Accepted Answer

1.5

Answer

12

Answer

1.2

Answer

0.67

Question 21

A random sample of 16 bags has a mean weight of 52 grams and a standard deviation of 8 grams. What is the t-statistic for testing H₀: μ = 50 grams?

Accepted Answer

1.0

Answer

4.0

Answer

2.0

Answer

0.25

Question 22

Adult heights in a population are approximately normal with mean 170 cm and standard deviation 8 cm. About what percentage of adults are taller than 186 cm?

Accepted Answer

2.5%

Answer

5%

Answer

16%

Answer

47.5%

Question 23

A company tests H₀: p = 0.10 against Hₐ: p < 0.10, where p is the proportion of defective parts after a new process. What would a Type I error be in this context?

Accepted Answer

Concluding the new process lowers the defect rate when it really does not

Answer

Concluding the new process does not lower the defect rate when it really does

Answer

Concluding the defect rate is exactly 0.10

Answer

Taking a sample that is not random

Question 24

A residual plot for a linear regression shows a clear U-shaped curve. What does this suggest?

Accepted Answer

A linear model is not appropriate, because the relationship is curved.

Answer

The linear model fits well, because the residuals are both positive and negative.

Answer

The correlation must be close to zero.

Answer

There must be an outlier in the data.

Question 25

Which of these variables is categorical?

Accepted Answer

A person’s ZIP code

Answer

A person’s number of siblings

Answer

A person’s height in centimeters

Answer

A person’s time to run one mile

Free AP® Statistics Practice Test (2026)

The practice test

Create a free account to see your score and every explanation

How you did on the Statistics practice test

By topic

Every question, with the explanation

Ready for the real exam?

More free AP practice tests 35

Not sure where to start?