Getting ready for the AP Statistics exam? These 20 free practice questions cover every unit of the course, from describing data to inference and regression, each with a clear explanation. Try each question on your own first, then tap Show answer to check your thinking.
The questions are written in the style of the multiple-choice section of the exam. Keep a calculator handy, just as you will on test day, but notice how many questions are really about reasoning and interpretation rather than arithmetic.
What the AP Statistics exam covers
- Exploring one-variable data and collecting data: types of variables, graphs, center and spread, sampling methods and experimental design
- Probability, random variables and probability distributions: probability rules, two-way tables, binomial and normal distributions, expected value, sampling distributions and the Central Limit Theorem
- Inference for categorical data (proportions): confidence intervals and significance tests for proportions, p-values, Type I and Type II errors, and chi-square tests
- Inference for quantitative data (means): one-sample, paired and two-sample t-intervals and t-tests, and the conditions behind them
- Regression analysis: scatterplots, correlation, the least-squares regression line, residuals, influential points and extrapolation
How to use these questions
Work through the questions without notes, the way you would on test day. Keep track of the ones you miss, and note which unit each one comes from. Two or three misses in the same unit is a sign to review that unit before moving on.
Don’t just check whether you got the right letter. Read every explanation, even for questions you answered correctly. AP Statistics questions often hinge on interpretation in context, such as what a p-value or confidence interval actually means, so the reasoning matters as much as the calculation.
Practice questions
Question 1
A radio station asks listeners to call in and say whether they support a new city curfew for teenagers. Of the 400 people who call, 78% oppose the curfew. Which of the following is the biggest problem with using this result to describe all city residents?
A. The sample of 400 is too small to draw any conclusion
B. The survey is a stratified random sample, so the results are biased
C. The survey is an experiment without a control group
D. The survey relies on voluntary response, so people with strong opinions are more likely to call in
E. The result should have been reported as a mean instead of a percentage
Show answer
Answer: D. Callers chose themselves, which is voluntary response. People who feel strongly (usually negatively) are the most likely to respond, so the 78% probably overstates opposition. A sample of 400 is plenty large; the problem is how it was chosen, not its size.
Question 2
The ages of the six members of a book club are 34, 38, 41, 45, 47 and 91. If the member who is 91 leaves the club, how do the mean and median ages change?
A. The mean decreases by a lot, and the median decreases only slightly
B. The median decreases by a lot, and the mean decreases only slightly
C. Both the mean and the median stay the same
D. The mean decreases, and the median increases
E. The mean stays the same, and the median decreases
Show answer
Answer: A. With all six members, the mean is 296/6 ≈ 49.3 and the median is (41 + 45)/2 = 43. Without the 91-year-old, the mean is 205/5 = 41 and the median is 41. The mean drops by about 8 years but the median drops by only 2, because the median is resistant to extreme values and the mean is not.
Question 3
A basketball player makes 80% of her free throws, and her shots are independent. What is the probability that she misses at least one of her next 3 free throws?
A. 0.008
B. 0.200
C. 0.488
D. 0.512
E. 0.600
Show answer
Answer: C. Use the complement. P(makes all 3) = 0.83 = 0.512, so P(misses at least one) = 1 − 0.512 = 0.488. The trap answer 0.512 is the probability she makes all three, and 0.008 is the probability she misses all three.
Question 4
The weights of apples in a large orchard have mean 150 grams and standard deviation 20 grams. A random sample of 25 apples is selected. What is the standard deviation of the sampling distribution of the sample mean weight?
A. 0.8 grams
B. 4 grams
C. 20 grams
D. 30 grams
E. 150 grams
Show answer
Answer: B. The standard deviation of the sample mean is σ/√n = 20/√25 = 20/5 = 4 grams. A common mistake is dividing by n instead of √n, which gives 0.8 grams.
Question 5
A student council tests H0: p = 0.50 versus Ha: p > 0.50, where p is the proportion of all students at the school who prefer a later start time. A random sample gives a p-value of 0.04. Which is the correct interpretation of this p-value?
A. There is a 4% chance that the null hypothesis is true
B. There is a 4% chance that the alternative hypothesis is true
C. 4% of students at the school prefer a later start time
D. If the true proportion is greater than 0.50, there is a 4% chance of getting the observed sample result
E. If the true proportion is 0.50, there is about a 4% chance of getting a sample proportion as large as or larger than the one observed, by chance alone
Show answer
Answer: E. A p-value is a probability calculated assuming the null hypothesis is true: it tells you how likely a result at least as extreme as the one observed would be if p really were 0.50. It is not the probability that either hypothesis is true.
Question 6
A factory checks whether its defect rate has risen above the acceptable level. It tests H0: p = 0.02 versus Ha: p > 0.02. If the test gives convincing evidence that the rate is too high, the production line is shut down for repairs. Which of the following describes a Type II error in this context?
A. Shutting down the line when the defect rate is actually 0.02
B. Not shutting down the line when the defect rate is actually greater than 0.02
C. Shutting down the line when the defect rate is actually greater than 0.02
D. Not shutting down the line when the defect rate is actually 0.02
E. Taking a sample that is too small to find any defects
Show answer
Answer: B. A Type II error is failing to reject a null hypothesis that is false. Here that means the defect rate really is above 0.02, but the test does not detect it, so the line keeps running. Choice A is a Type I error, and choices C and D are correct decisions.
Question 7
In a randomized experiment, volunteers were randomly assigned to drink either a caffeinated or a decaffeinated beverage before a reaction-time test. A 95% confidence interval for the difference in mean reaction times (caffeine minus no caffeine), in milliseconds, is (−18.4, 6.2). Which conclusion is best supported?
A. Caffeine has no effect at all on reaction time
B. Caffeine lowers mean reaction time by exactly 6.1 milliseconds
C. Because 0 is in the interval, the data do not give convincing evidence of a difference in mean reaction times
D. 95% of volunteers had a difference between −18.4 and 6.2 milliseconds
E. Because most of the interval is negative, caffeine reduces reaction time
Show answer
Answer: C. The interval includes 0, so "no difference" is a plausible value for the true difference in means. That means the data do not give convincing evidence of a difference. It does not prove there is no effect, and the interval is about the difference in means, not about individual volunteers.
Question 8
A random sample of 16 bags of chips has a mean weight of 28.4 grams and a standard deviation of 1.2 grams. To test H0: μ = 28 versus Ha: μ > 28, what is the value of the test statistic?
A. 0.33
B. 0.40
C. 1.20
D. 1.33
E. 5.33
Show answer
Answer: D. t = (x̄ − μ0)/(s/√n) = (28.4 − 28)/(1.2/√16) = 0.4/0.3 ≈ 1.33. Choice A forgets to divide s by √n, and choice E divides by n instead of √n.
Question 9
For a group of students, the least-squares regression line relating final exam score to number of absences is ŷ = 92 − 2.5x, where x is the number of absences. A student with 6 absences scored 80 on the final exam. What is this student’s residual?
A. −3
B. 3
C. 12
D. 77
E. 80
Show answer
Answer: B. The predicted score is 92 − 2.5(6) = 92 − 15 = 77. Residual = observed − predicted = 80 − 77 = 3. A positive residual means the student scored 3 points higher than the line predicts. Choice A reverses the order of subtraction.
Question 10
A least-squares regression of monthly electric bill (in dollars) on average monthly temperature for 30 homes has r2 = 0.49. Which is the correct interpretation of r2?
A. About 49% of the variation in monthly electric bills is explained by the linear relationship with average monthly temperature
B. The correlation between electric bill and temperature is 0.49
C. About 49% of the predictions made by the line are exactly correct
D. Temperature causes 49% of each electric bill
E. The slope of the regression line is 0.49
Show answer
Answer: A. r2 is the proportion of the variation in the response variable that is explained by the linear model. The correlation itself would be ±0.7 (the square root of 0.49), and regression on observational data cannot show causation.
More practice from the AP+ workbook
These next 10 questions come straight from our AP+ Review Workbook, with the same explanations you’ll find in its answer key.
Question 11
Researchers group garden plots by soil type and then randomly assign a new fertilizer or the standard fertilizer to plots within each soil type. This design is:
A. A randomized block design
B. A completely randomized design
C. A stratified random sample
D. An observational study
Show answer
Answer: A. The plots are first grouped into blocks of similar plots (by soil type), and then treatments are randomly assigned separately within each block. That is a randomized block design. It is an experiment, not a sample, because treatments are assigned.
Question 12
A teacher adds 5 points to every student’s quiz score. How are the mean and standard deviation affected?
A. Both increase by 5
B. The mean is unchanged and the standard deviation increases by 5
C. Both are unchanged
D. The mean increases by 5 and the standard deviation is unchanged
Show answer
Answer: D. Adding a constant shifts every value by the same amount, so the center shifts up by 5. The distances between the values do not change, so the spread, including the standard deviation, stays the same.
Question 13
Of 80 students, 30 take Spanish. Of those 30, 12 also take art. For a randomly chosen Spanish student, what is P(takes art)?
A. 0.60
B. 0.40
C. 0.375
D. 0.15
Show answer
Answer: B. The condition is "takes Spanish," so the denominator is the 30 Spanish students, not all 80 students. P(art | Spanish) = 12/30 = 0.40.
Question 14
A binomial random variable has n = 5 and p = 0.3. What is P(X = 2)?
A. 0.0900
B. 0.1323
C. 0.3087
D. 0.6000
Show answer
Answer: C. Use the binomial formula: P(X = 2) = C(5, 2)(0.3)2(0.7)3 = 10(0.09)(0.343) = 0.3087. Forgetting the C(5, 2) = 10 arrangements gives 0.0309, and leaving out the failures gives 0.0900.
Question 15
A pollster wants a 95% confidence interval for a proportion with a margin of error of at most 0.03 and has no prior estimate of p. What is the smallest sample size needed?
A. 1,112
B. 1,068
C. 752
D. 385
Show answer
Answer: B. With no prior estimate, use p* = 0.5, which gives the largest possible margin of error. Then n = (1.96/0.03)2 × 0.25 ≈ 1,067.1. Always round up to guarantee the margin of error, so n = 1,068.
Question 16
A chi-square test uses a two-way table with 3 rows and 4 columns. How many degrees of freedom does the test have?
A. 6
B. 7
C. 11
D. 12
Show answer
Answer: A. For a chi-square test on a two-way table, df = (rows − 1)(columns − 1) = (3 − 1)(4 − 1) = 2 × 3 = 6.
Question 17
A study measures weight loss for the same 15 participants before and after a 6-week program. The correct procedure is:
A. Two-sample t-test
B. Two-proportion z-test
C. One-sample t-test on the differences
D. Chi-square test
Show answer
Answer: C. The same 15 participants are measured twice, so the data are paired. The analysis is a one-sample t-procedure on the before-minus-after differences. A two-sample t-test would wrongly treat the two sets of measurements as independent groups.
Question 18
What critical value t* is used for a 95% confidence interval with 15 degrees of freedom?
A. 2.947
B. 2.131
C. 1.960
D. 1.753
Show answer
Answer: B. From the t-table (or invT(0.975, 15) on a calculator), t* = 2.131. The value 1.960 is the z* for 95% confidence, which is used for proportions, not for means with an estimated standard deviation.
Question 19
For a set of data, r = 0.6, the standard deviation of x is 4, and the standard deviation of y is 10. What is the slope of the least-squares regression line?
A. 6.0
B. 2.4
C. 1.5
D. 0.24
Show answer
Answer: C. The slope of the least-squares line is b = r(sy/sx) = 0.6(10/4) = 0.6(2.5) = 1.5. Using sx/sy instead gives 0.24.
Question 20
Heights in a study are converted from inches to centimeters. What happens to the correlation between height and weight?
A. It increases by a factor of 2.54
B. It decreases by a factor of 2.54
C. It becomes undefined
D. It stays the same
Show answer
Answer: D. Correlation has no units, so changing the units of measurement does not change it. Converting inches to centimeters changes the numbers but not the strength or direction of the linear relationship.
How did you do?
If you got 17 or more right, you have a strong foundation. Focus your review on the explanations for any you missed. If you got 12 to 16 right, you’re on track, but a few units need more practice. If you got 11 or fewer right, start with the unit reviews before doing more practice questions.
Our AP+ Statistics Review Workbook covers every unit with clear summaries, worked examples, condition checks for every inference procedure, statistical writing practice and two full-length practice exams with answers and explanations. It’s available as an instant PDF download or a paperback.
See the AP+ Statistics Review Workbook →
Studying for more than one AP exam? Browse the full AP+ Exam Prep series.
Frequently asked questions
Are these questions like the real AP Statistics exam?
They’re written in the style of the multiple-choice section and cover the same units and skills. Official practice materials from the College Board are also worth using alongside them.
What’s the best way to study for AP Statistics?
Review one unit at a time, practice choosing the right procedure before you calculate anything, and always state conditions and conclusions in context. Reading the explanation for every question, including ones you get right, builds the reasoning the exam rewards.
When is the AP Statistics exam?
AP exams are given each May. Check the College Board’s AP website for the current exam schedule.
AP is a registered trademark of the College Board, which was not involved in the production of, and does not endorse, this page or our workbooks.