AP Statistics · 228 questions from 38 exams
Past free-response questions
Every free-response question College Board has released for AP Statistics from 1998 to 2026. Each one opens College Board's own question beside a space to write your answer, part by part, and then College Board's scoring guidelines so you can score it yourself.
Your answers and scores stay in this browser and are never sent anywhere.
2026
This exam had six free-response questions, each scored from 0 to 4. Its Question 6, the Investigative Task, is no longer part of the exam. The current exam has 4 free-response questions in 90 minutes. The skills these questions practice still count.
- Question 1 · Focus on Exploring Data · 4 points Comparing weights of two goat breeds Find a five-number summary from a list, compare center and spread with a second breed's box plot, and explain a feature of shape that a stem-and-leaf plot shows but a box plot hides. Unit 1
- Question 2 · Focus on Sampling and Experimental Design · 4 points Coffee grounds and rosebush flowers Name the treatments, units and response in a greenhouse experiment, describe a random assignment giving equal group sizes, and explain what a statistically significant result means here. Unit 1, Unit 3
- Question 3 · Focus on Probability and Sampling Distributions · 4 points How long a team song performance lasts Find a normal probability for one performance, use it in a binomial probability over ten games, then find and interpret the mean and standard deviation of the wait for the first long performance. Unit 2
- Question 4 · Focus on Inference · 4 points Orange yields under two fertilizers Carry out a full significance test of whether mean orange counts differ between trees randomly given two fertilizer brands. Unit 4
- Question 5 · Multi-Focus · 4 points Age groups of pro athletes by sport Find a marginal and a conditional probability from a two-way table, match them to a mosaic plot, check two events for being disjoint or independent, and decide if a chi-square test fits census data. Unit 2, Unit 3
- Question 6 · Investigative Task, no longer on the exam · 4 points Hits, runs and team salaries in baseball Describe a scatterplot and make a prediction, compare a labeled team and the strength of two groups, build a confidence interval and a prediction interval, and explain why one is wider. Unit 5, Unit 2
2025
This exam had six free-response questions, each scored from 0 to 4. Its Question 6, the Investigative Task, is no longer part of the exam. The current exam has 4 free-response questions in 90 minutes. The skills these questions practice still count.
- Question 1 · Focus on Exploring Data · 4 points Comparing gas mileage from two countries Compare two box plots of gas mileage, reason whether one sample's mean sits above or below a value, and work out the range and a possible median if the two samples were pooled. Unit 1
- Question 2 · Focus on Sampling and Experimental Design · 4 points Sampling a cabbage field for aphids Judge a convenience choice of region, decide whether picking one row near a river would overestimate or underestimate damage, and explain how to choose one random region from every row. Unit 1
- Question 3 · Focus on Probability and Sampling Distributions · 4 points Rock songs on a restaurant playlist Find probabilities for one and two random songs, define and name the distribution of rock songs in an hour along with its mean, then find a probability and judge whether a result is unusual. Unit 2
- Question 4 · Focus on Inference · 4 points Students using a homework help app Carry out a full significance test of whether a school's proportion of weekly app users is higher than the national figure, using one random sample. Unit 3
- Question 5 · Multi-Focus · 4 points Number of bedrooms in new houses Use a distribution of bedroom counts to find a probability and a mean, write hypotheses for a test about the mean, describe a Type I error, and use a confidence interval to reach the test's conclusion. Unit 4, Unit 3, Unit 2
- Question 6 · Investigative Task, no longer on the exam · 4 points Reading scores by time of day State a conclusion from a two-sample test, explain why a paired test would be wrong here, then compute and interpret an effect size and reason how larger spread would change it. Unit 4
2024
This exam had six free-response questions, each scored from 0 to 4. Its Question 6, the Investigative Task, is no longer part of the exam. The current exam has 4 free-response questions in 90 minutes. The skills these questions practice still count.
- Question 1 · Focus on Inference · 4 points Interest in online fitness classes by age Run a complete significance test comparing the proportion of younger and older gym members who want online classes, using two independent random samples. Unit 3
- Question 2 · Focus on Exploring Data · 4 points Water bottle sales at different schools Finish segmented bar graphs for two schools, explain why relative frequencies alone cannot show which school sold more of one size, and read a mosaic plot for both proportion and count. Unit 2, Unit 1
- Question 3 · Focus on Sampling and Experimental Design · 4 points Car mileage and an autopilot feature Decide whether a survey of car owners is an experiment or an observational study, describe how to randomly assign autopilot days, and say what change would let results extend to a whole club. Unit 1
- Question 4 · Focus on Probability and Sampling Distributions · 4 points Opening geodes to find a red crystal Find the mean and standard deviation of the wait for a first success, complete a probability distribution for a player who stops after at most four tries, and compute and interpret its mean. Unit 2
- Question 5 · Multi-Focus · 4 points Baseball card collectors and rare cards Use a two-way table to find a joint and a conditional probability, name the right test and its hypotheses for an association, and draw a conclusion from a given p-value. Unit 3, Unit 2
- Question 6 · Investigative Task, no longer on the exam · 4 points Whistle prices and a skewness measure Pick an interval procedure and its parameter, judge shape and outliers from summary values, compute a new skewness coefficient and read it off a chart, then decide if the normality condition holds. Unit 1, Unit 4
2023
This exam had six free-response questions, each scored from 0 to 4. Its Question 6, the Investigative Task, is no longer part of the exam. The current exam has 4 free-response questions in 90 minutes. The skills these questions practice still count.
- Question 1 · Focus on Exploring Data · 4 points Oxygen levels in cold and warm streams Describe a histogram of oxygen readings, build a box plot from a table of summary values, then argue which group of streams looks healthier using features of both distributions. Unit 1
- Question 2 · Focus on Sampling and Experimental Design · 4 points Testing fiber concrete for driveway cracking Name the units, treatments and response in a driveway experiment, explain a way to randomly split the 60 driveways between the two concretes, and say what random assignment lets the developer conclude. Unit 1
- Question 3 · Focus on Probability and Sampling Distributions · 4 points Cash prizes hidden in bath fizzies Use a prize probability table to fill in a missing probability, find an at-least probability and a conditional probability, then compute and interpret the expected prize and convert it to euros. Unit 2
- Question 4 · Focus on Inference · 4 points Omega-3 supplement and irritability scores Each patient tried both the supplement and a placebo. Carry out a full significance test on the paired differences to decide whether the supplement lowers mean irritability. Unit 4
- Question 5 · Multi-Focus · 4 points Predicting elk weight from chest size Describe a scatterplot, use a given regression line to predict a weight and find a residual, interpret the slope, then find a p-value and draw a conclusion from a test about the slope. Unit 5
- Question 6 · Investigative Task, no longer on the exam · 4 points Checking a gold-plating machine with tiny samples Find normal probabilities for one necklace and for a mean of two, judge whether a sample result is surprising, describe simulated sampling distributions of the range, and decide whether the machine is off. Unit 2, Unit 4, Unit 3
Earlier exams
College Board no longer posts these on its site. Each one opens College Board's own PDF as the Internet Archive saved it, with the scoring guidelines saved the same way.
2022
This exam had six free-response questions, each scored from 0 to 4. Its Question 6, the Investigative Task, is no longer part of the exam. The current exam has 4 free-response questions in 90 minutes. The skills these questions practice still count.
- Question 1 · Focus on Exploring Data · 4 points Bullfrog length and mass regression Describe the scatterplot of frog mass against length, interpret the slope and r squared of the fitted line, then find the frog with the biggest residual and say whether the line over or under predicts its mass. Unit 5
- Question 2 · Focus on Collecting Data · 4 points Twin acne drug matched pairs experiment Name the treatments, units and response in a twin study of an acne drug, explain why pairing twins helps compared with a completely randomized design, and describe how to randomize within pairs. Unit 1
- Question 3 · Focus on Probability and Sampling Distributions · 4 points Shampoo bottle fills and crate rejection Use a normal model to find the chance a bottle is underfilled, set up a binomial count of underfilled bottles in a box of ten to find the chance a crate is rejected, and compare two machine settings. Unit 2
- Question 4 · Focus on Inference · 4 points Teen streaming habits confidence interval Build and interpret a 95 percent interval for the share of teens who stream every day, then use the interval to decide whether that share differs from one half. Unit 3
- Question 5 · Multi-Focus · 4 points Dark versus white chocolate blood pressure Find and compare medians from two dotplots, explain why a positive difference in sample means alone does not settle the question, and use a simulated null distribution to judge significance. Unit 1, Unit 4, Unit 3
- Question 6 · Investigative Task, no longer on the exam · 4 points Allergy clinics and a reversed comparison Turn a two way table into conditional relative frequencies to pick the better clinic, explain why the observational design blocks a causal claim, then use a mosaic plot split by allergy severity to explain why the comparison flips. Unit 2, Unit 1
2021
This exam had six free-response questions, each scored from 0 to 4. Its Question 6, the Investigative Task, is no longer part of the exam. The current exam has 4 free-response questions in 90 minutes. The skills these questions practice still count.
- Question 1 · Focus on Exploring Data · 4 points Hospital stay length outlier rules Find the five number summary for lengths of stay, flag outliers using both the IQR rule and the two standard deviation rule, and explain why the two rules can disagree for right skewed data. Unit 1
- Question 2 · Focus on Collecting Data · 4 points Walking and cholesterol study design Explain how self reported walking journals could bias the data, why a representative sample matters, and whether a significant result from this observational study supports a causal claim. Unit 1
- Question 3 · Focus on Probability and Sampling Distributions · 4 points Weekly gift card drawing probabilities Define a binomial count of wins for one employee over a year, find the chance of at least one win and the expected number of wins, and judge whether never winning is evidence the drawing is unfair. Unit 2
- Question 4 · Focus on Inference · 4 points Coupon offer one proportion test Run a one proportion significance test of whether more than 40 percent of past customers respond to a coupon, then name the possible error and its consequence in context. Unit 3
- Question 5 · Multi-Focus · 4 points Teen soft drinks across three cities Explain why raw counts are the wrong basis for comparing cities, draw a segmented bar graph of the proportions in each group, and name the right chi square test with its hypotheses. Unit 2, Unit 3
- Question 6 · Investigative Task, no longer on the exam · 4 points Baseball attendance in two stadiums Compare attendance boxplots for an old and a new stadium, compare trends over time, describe the link between wins and attendance, and explain how one variable could confound the others. Unit 1, Unit 5
2019
This exam had six free-response questions, each scored from 0 to 4. Its Question 6, the Investigative Task, is no longer part of the exam. The current exam has 4 free-response questions in 90 minutes. The skills these questions practice still count.
- Question 1 · 4 points Residence hall room sizes histogram and boxplot Describe a histogram of room sizes, check the summary statistics for outliers and sketch a boxplot, then name a feature of the shape the histogram shows but the boxplot hides. Unit 1
- Question 2 · 4 points Fungus spray experiment on insects Name the treatments, units and response in an experiment spraying insect containers with fungus mixtures, say whether there is a control group, and describe a balanced random assignment. Unit 1
- Question 3 · 4 points Taking medicine as prescribed probabilities Use a joint relative frequency table to find an intersection, a union and a conditional probability, check two events for independence, and find a binomial probability of at least four of five. Unit 2
- Question 4 · 4 points Herbicide resistant weeds two proportion test Carry out a two proportion significance test of whether the share of weeds resistant to an herbicide rose between two years. Unit 3
- Question 5 · 4 points Phone battery life and warranty value Use a normal model to find the time by which a quarter of batteries fail and the chance of failing within the warranty, then find the company's expected gain per warranty sold. Unit 2
- Question 6 · 4 points Apartment rents and a bootstrap interval Describe the population a website sample of rents represents, explain why the mean is a poor summary for skewed rents, describe how a sampling distribution of medians could be built, then read percentiles from a bootstrap table to make and interpret an interval for the median. Unit 1, Unit 2, Unit 3
2018
This exam had six free-response questions, each scored from 0 to 4. Its Question 6, the Investigative Task, is no longer part of the exam. The current exam has 4 free-response questions in 90 minutes. The skills these questions practice still count.
- Question 1 · 4 points Checkout line length and wait time Read the intercept and r squared from regression output and interpret both in context, then circle the outlier on the plot and say why it stands out. Unit 5
- Question 2 · 4 points Recycling survey bias and randomized response Work back from a confidence interval to the sample size, explain how face to face questioning could bias the estimate, and use a coin flip response scheme to find an expected count and a new estimate. Unit 3, Unit 1, Unit 2
- Question 3 · 4 points Left handed children from multiple births Combine conditional percentages to find the chance a child is left handed, reverse the condition to find the chance a left handed child is from a multiple birth, and find a binomial probability for a sample of 20. Unit 2
- Question 4 · 4 points ACL surgery recovery time experiment Explain whether random assignment supports a causal conclusion, then carry out a two sample test of whether the new procedure lowers mean recovery time. Unit 1, Unit 4
- Question 5 · 4 points Teaching experience at two high schools Match each school to its median using the histograms, combine two groups to find an overall mean, and use the histogram to find the chance a teacher falls within one standard deviation of the mean. Unit 1, Unit 2
- Question 6 · 4 points Employee blood pressure and test power Describe a Type II error, find the sample means that would reject the null, compute the chance of rejecting when the true mean is higher, name that probability, and explain how a bigger sample changes it. Unit 3, Unit 4
2017
This exam had six free-response questions, each scored from 0 to 4. Its Question 6, the Investigative Task, is no longer part of the exam. The current exam has 4 free-response questions in 90 minutes. The skills these questions practice still count.
- Question 1 · 4 points Gray wolf length and weight regression Explain what positive, linear and strong mean for this scatterplot, interpret the slope of the regression line, and use a residual to recover one wolf's actual weight. Unit 5
- Question 2 · 4 points Water cups filled with soda Build and interpret a 95 percent interval for the share of water cup customers who take soda, then scale it to an interval for the monthly cost. Unit 3
- Question 3 · 4 points Melon diameters from two distributors Use a normal model for one distributor's melons, combine the two distributors to find the overall chance a melon is large, and then find the chance a large melon came from the first distributor. Unit 2
- Question 4 · 4 points Pottery chemicals across three sites Compare boxplots of one chemical across three sites, then use the boxplots to pick the likely site for a piece of pottery and the single chemical that best tells the sites apart. Unit 1
- Question 5 · 4 points Schizophrenia diagnosis age and gender Carry out a chi square test of whether age group at diagnosis is associated with gender. Unit 3
- Question 6 · 4 points Coin flip versus chip random assignment Find the probability of each possible group arrangement under a sequential coin flip method and under a chip method, and decide which method suits an experiment where students enter before teachers. Unit 1, Unit 2
2016
This exam had six free-response questions, each scored from 0 to 4. Its Question 6, the Investigative Task, is no longer part of the exam. The current exam has 4 free-response questions in 90 minutes. The skills these questions practice still count.
- Question 1 · 4 points Server tips histogram and changing one value Describe the distribution of a day's tips from a histogram and explain how raising one tip would change the mean and the median. Unit 1
- Question 2 · 4 points Snack ads and children's choices Carry out a chi square test of whether ad type and snack choice are associated in a randomized experiment, then describe what each ad did to the choices. Unit 3, Unit 2
- Question 3 · 4 points Smoking and Alzheimer's study Name the explanatory and response variables, decide whether the study is observational or an experiment, and explain how exercise habits could confound the result. Unit 1
- Question 4 · 4 points Model rocket igniter failure testing Find the chance 30 igniters in a row work at a 15 percent failure rate, find the chance the first failure comes on the next one or two given that streak, and judge whether the streak suggests a lower failure rate. Unit 2, Unit 3
- Question 5 · 4 points Environment versus economy poll Build and interpret a 95 percent interval for the share choosing the economy statement, explain why the large counts condition matters, and explain why a two sample interval does not fit two shares from one sample. Unit 3
- Question 6 · 4 points College semesters and starting salary Judge whether a scatterplot supports a newspaper claim, interpret the slope from regression output, then use a scatterplot split by major to describe one group, compare medians and suggest a better claim. Unit 5, Unit 1
2015
This exam had six free-response questions, each scored from 0 to 4. Its Question 6, the Investigative Task, is no longer part of the exam. The current exam has 4 free-response questions in 90 minutes. The skills these questions practice still count.
- Question 1 · 4 points Accountant salaries at two corporations Compare salary boxplots for two companies and use them to give one reason to choose each job. Unit 1
- Question 2 · 4 points Restaurant discount program and margin of error Use a given confidence interval to judge two claims about the discount rate, find the margin of error for a sample four times larger, and draw a new conclusion from it. Unit 3
- Question 3 · 4 points Working ATMs probability distribution From a probability table find the chance at least one machine works, the expected number working, a conditional probability, and how the expected value changes given at least one works. Unit 2
- Question 4 · 4 points Low dose aspirin and colon cancer Carry out a two proportion significance test of whether daily aspirin lowers the chance of colon cancer in a randomized experiment. Unit 3
- Question 5 · 4 points Arm span versus height body shapes Describe the scatterplot of arm span against height, decide whether the regression line or the line y equals x helps classify body shapes and count each shape, then predict arm span for a given height. Unit 5
- Question 6 · 4 points Tortilla diameters and two sampling methods Compare a simple random sample of all tortillas with sampling from one randomly chosen production line, looking at representativeness, spread within a sample, the sampling distribution of the mean and which method lands closer to the target on a given day. Unit 1, Unit 2, Unit 3, Unit 4
2014
This exam had six free-response questions, each scored from 0 to 4. Its Question 6, the Investigative Task, is no longer part of the exam. The current exam has 4 free-response questions in 90 minutes. The skills these questions practice still count.
- Question 1 · 4 points Campus residence and club participation Find conditional proportions from a two-way table, describe the association shown in a segmented bar graph, and state a conclusion from a given chi-square p-value. Unit 2, Unit 3
- Question 2 · 4 points Were the convention travelers really chosen randomly? Compute the chance that three people drawn from six men and three women are all women, judge the manager's claim, and decide whether a dice simulation models the selection correctly. Unit 2
- Question 3 · 4 points School absences and state funding Use a normal model to find the chance absences exceed a cutoff, compare that with a plan based on the mean of three days, and find a probability for three independent day choices. Unit 2, Unit 4
- Question 4 · 4 points Estimating income of a reunion class Explain why the median can be a better summary than the mean for incomes, then choose between a large voluntary email survey and a small random phone sample, explaining the effect on the estimate. Unit 1
- Question 5 · 4 points Do women pay more for cars? Carry out a paired t test on matched purchase prices to decide whether women pay more on average than men do when buying an identical model. Unit 4
- Question 6 · 4 points Predicting fuel use from car measurements Compute and interpret a residual, locate a car on a residual plot and explain a residual near zero, compare two residual plots, and pick the second variable that would improve the prediction. Unit 5
2013
This exam had six free-response questions, each scored from 0 to 4. Its Question 6, the Investigative Task, is no longer part of the exam. The current exam has 4 free-response questions in 90 minutes. The skills these questions practice still count.
- Question 1 · 4 points Lead levels in crows Read a stemplot to find the proportion of crows above a cutoff, then build and interpret a 95 percent t interval for the average amount of lead. Unit 4, Unit 1
- Question 2 · 4 points Surveying students about the campus Explain the bias in a sample taken at a football game, describe how to draw a simple random sample by computer, and say when stratifying by campus beats stratifying by gender. Unit 1
- Question 3 · 4 points Weights of egg cartons Find a normal probability for a carton's weight, then work out the mean and standard deviation of a single egg's weight from the carton and container information. Unit 2
- Question 4 · 4 points Age group and eating vegetables Carry out a chi-square test to decide whether age group is associated with eating at least five daily servings of fruit and vegetables. Unit 3
- Question 5 · 4 points Meditation and blood pressure in retirees Explain why an observational study cannot show causation, say why a normal approximation fails for small samples, and draw a conclusion from a simulated null distribution. Unit 3, Unit 1
- Question 6 · 4 points Typhoon counts and moving averages Compare yearly typhoon counts in two ocean regions, describe trends over time, compute a missing moving average and add it to a graph, and explain what smoothing reveals and hides. Unit 1, Unit 5
2012
This exam had six free-response questions, each scored from 0 to 4. Its Question 6, the Investigative Task, is no longer part of the exam. The current exam has 4 free-response questions in 90 minutes. The skills these questions practice still count.
- Question 1 · 4 points Price and quality of sewing machines Describe the association in a scatterplot, identify the point that most affects a linear fit, and circle the machines no other machine beats on both price and quality. Unit 5
- Question 2 · 4 points A charity spinner game Fill in a probability distribution for the charity's net gain, find its expected value, find how many plays are needed to expect a target, and use a normal model for the total over many plays. Unit 2
- Question 3 · 4 points Household size in 1950 and 2000 Compare two histograms of household size, then state and check the conditions for a two-sample t interval. Unit 1, Unit 4
- Question 4 · 4 points Opinions on TV commercials over a year Carry out a two-sample z test to decide whether the proportion of adults who find commercials effective changed between two surveys. Unit 3
- Question 5 · 4 points City fitness test and funding Describe a Type II error and its consequence, interpret a large p-value, and identify the main flaw in using volunteers as the sample. Unit 3, Unit 1
- Question 6 · Investigative Task, no longer on the exam · 4 points Two ways to estimate soft drink use Describe how to draw a simple random sample, compute standard errors for a simple random sample mean and for a stratified weighted estimator, and use dotplots to explain why stratifying helped. Unit 3, Unit 1, Unit 4
2011
This exam had six free-response questions, each scored from 0 to 4. Its Question 6, the Investigative Task, is no longer part of the exam. The current exam has 4 free-response questions in 90 minutes. The skills these questions practice still count.
- Question 1 · 4 points Evaluating athletes on speed and strength Judge from the mean, the standard deviation and the minimum whether running times can be normal, compute and interpret a z-score, and use standardized scores to choose between two players. Unit 1, Unit 2
- Question 2 · 4 points Party registration by gender Find a conditional probability from a two-way table, check whether two events are independent, and complete a segmented bar graph for a township where party and gender are independent. Unit 2
- Question 3 · 4 points Choosing apartments for new carpet Describe how to pick eight apartments with a cluster sample by floor, and give an advantage of stratifying by whether children live there. Unit 1
- Question 4 · 4 points Does a cholesterol drug help? Carry out a two-sample t test on cholesterol reductions to decide whether the drug group improved more than the placebo group. Unit 4
- Question 5 · 4 points Wind speed and windmill output Read regression output to write the least squares line, predict a change in output, report the proportion of variation explained, and judge whether output is related to wind speed. Unit 5
- Question 6 · 4 points How many students really know the answer? Build and interpret a 99 percent interval for a proportion, fill in a tree diagram for knowing versus guessing, write the chance of a correct answer in terms of k, and convert the interval into one for k. Unit 3, Unit 2
2011, Form B
This exam had six free-response questions, each scored from 0 to 4. Its Question 6, the Investigative Task, is no longer part of the exam. The current exam has 4 free-response questions in 90 minutes. The skills these questions practice still count.
- Question 1 · 4 points Pupil to teacher ratios by region Estimate medians from two histograms, compare the two distributions, and predict how the means compare. Unit 1
- Question 2 · 4 points A drug paired with fear of heights therapy Decide whether the study is an experiment, judge whether the result supports a comparison it never tested, and explain how letting therapists assign treatments could mislead. Unit 1
- Question 3 · 4 points Airline seat upgrades for a frequent flier Find the chance the first upgrade comes after the third flight, find a binomial probability for 20 flights, and judge whether more than 20 upgrades in 104 flights would be surprising. Unit 2
- Question 4 · 4 points Part-time work and academic achievement State hypotheses for a chi-square test, check its conditions, draw a conclusion from the output, and describe which error could have been made. Unit 3
- Question 5 · 4 points Flu vaccine coverage estimate Build a 99 percent interval for a proportion and use it to judge a claimed rate, then find the sample size that keeps the margin of error at 0.02 or less. Unit 3
- Question 6 · Investigative Task, no longer on the exam · 4 points Grass buffer strips and nitrogen removal Interpret a regression slope, judge extrapolation, describe the sampling distribution of a mean at one width, and use interval plots to pick the study design that estimates the slope better. Unit 5, Unit 4, Unit 1
2010
This exam had six free-response questions, each scored from 0 to 4. Its Question 6, the Investigative Task, is no longer part of the exam. The current exam has 4 free-response questions in 90 minutes. The skills these questions practice still count.
- Question 1 · 4 points Garlic oil as a bird repellent Name the treatments, experimental units and response in an experiment, then graph mean consumption against concentration and judge whether a linear model fits. Unit 1, Unit 5
- Question 2 · 4 points Total airtime for radio songs Give the shape, center and spread of the distribution of sample mean length for 40 songs, then find the approximate chance their total time is more than the airtime available. Unit 2, Unit 4
- Question 3 · 4 points Dog ownership in a county Interpret a 95 percent confidence level, use an interval to judge a national claim, and work backward from the interval to the sample size. Unit 3
- Question 4 · 4 points Sampling owners of five car models Find the mean and standard deviation of how many owners of a rare model appear in a random sample, judge how likely a small count is, and design a sample that guarantees each model is represented. Unit 2, Unit 1
- Question 5 · 4 points Comparing fish lengths from two suppliers Carry out a two-sample t test to decide whether fish from one supplier are longer on average. Unit 4
- Question 6 · Investigative Task, no longer on the exam · 4 points Hurricane damage across coastal regions Sketch a display comparing damage by region and distance, describe the differences, compute average ranks and a rank-based statistic, and use simulated values to judge significance. Unit 1, Unit 2, Unit 3
2010, Form B
This exam had six free-response questions, each scored from 0 to 4. Its Question 6, the Investigative Task, is no longer part of the exam. The current exam has 4 free-response questions in 90 minutes. The skills these questions practice still count.
- Question 1 · 4 points Pesticide levels in three rivers Compare three boxplots, build a stemplot for one river, and name a feature the stemplot shows that the boxplot hides. Unit 1
- Question 2 · 4 points Surveying students about school meals Describe how to draw a simple random sample of 200 students, suggest a useful variable for stratifying, and give an advantage of stratifying. Unit 1
- Question 3 · 4 points Guessing on a test with a penalty Identify the distribution of correct guesses, show the expected score for a partly guessing student, and find the chance that student passes. Unit 2
- Question 4 · 4 points Who loaded the songs on a music player? Build and interpret a 90 percent interval for a proportion, and explain why sampling with or without replacement hardly matters here. Unit 3
- Question 5 · 4 points Education level and main news source Find a union and a conditional probability from a two-way table, check independence of two events, and name the right test and its degrees of freedom. Unit 2, Unit 3
- Question 6 · Investigative Task, no longer on the exam · 4 points House prices, size and swimming pools Interpret a regression slope and a residual, use residuals to estimate the price effect of a pool, judge a difference in slopes from an interval, and compare two estimates of the pool effect. Unit 5
2009
This exam had six free-response questions, each scored from 0 to 4. Its Question 6, the Investigative Task, is no longer part of the exam. The current exam has 4 free-response questions in 90 minutes. The skills these questions practice still count.
- Question 1 · 4 points Gender and part-time job experience Build a graph showing how job experience relates to gender in a sample of seniors, describe what it shows, then name the right test and write its hypotheses. Unit 2, Unit 3
- Question 2 · 4 points Tire stopping distances and normal probability Find a percentile of a normal distribution of stopping distances, use it in a binomial probability for five cars, and find the chance a sample mean of five cars is at least 130 feet. Unit 2
- Question 3 · 4 points Frog dissection versus computer simulation Describe how to randomly split 24 students into two equal groups, then explain with an example how letting students pick their program could spoil the comparison. Unit 1
- Question 4 · 4 points Response times at two fire stations Build and interpret a 95 percent interval estimate of how far apart the two mean response times are, then decide whether it backs the claim that the means differ. Unit 4
- Question 5 · 4 points Chest compression study p-value Explain what a given p-value means for a randomized study of two first-aid methods, state a conclusion at the 0.05 level, and name the possible error and its consequence. Unit 3
- Question 6 · Investigative Task, no longer on the exam · 4 points Measuring skewness in fuel efficiency data Set up hypotheses about a car's mean mpg, then reason about a mean-to-median ratio as a skewness measure, judge it against a simulated distribution, and invent another skewness statistic from the five-number summary. Unit 4, Unit 1, Unit 2
2009, Form B
This exam had six free-response questions, each scored from 0 to 4. Its Question 6, the Investigative Task, is no longer part of the exam. The current exam has 4 free-response questions in 90 minutes. The skills these questions practice still count.
- Question 1 · 4 points State gasoline taxes on a boxplot Read the median and IQR off a boxplot of state gas taxes, marking how you found them, then say how both change when a fixed federal tax is added to every state. Unit 1
- Question 2 · 4 points Probabilities for an HIV screening test Use counts from a training run to estimate a false positive rate, the share of positives that truly carry HIV, and the chance an HIV-free sample gets sent on for the more expensive test. Unit 2
- Question 3 · 4 points Cardiopump versus CPR survival rates State and check the conditions for comparing two survival proportions, then carry out a test of whether the cardiopump rate is higher. Unit 3
- Question 4 · 4 points Blocking birds by species Explain how to assign birds to two striped colorings in a design blocked by species, then name another way to raise the power of the experiment and why it works. Unit 1, Unit 3
- Question 5 · 4 points Juice bottle filling machine Run a t test on whether a filling machine's mean amount differs from its target, then use a simulated dotplot of sample standard deviations to judge whether the spread is too large. Unit 4, Unit 2, Unit 3
- Question 6 · Investigative Task, no longer on the exam · 4 points Relative risk for two disease treatments Decide whether the trial could be double-blind, build a confidence interval for a difference in survival proportions, then estimate a relative risk and turn a given interval for its logarithm into an interval for the ratio. Unit 3, Unit 1
2008
This exam had six free-response questions, each scored from 0 to 4. Its Question 6, the Investigative Task, is no longer part of the exam. The current exam has 4 free-response questions in 90 minutes. The skills these questions practice still count.
- Question 1 · 4 points Sugar content of breakfast cereals Compare boxplots of sugar per serving for two serving sizes, then explain what rescaled boxplots add and how the means should compare. Unit 1
- Question 2 · 4 points Nonresponse in a year-round school survey Explain how low response could distort a school survey, whether mailing a second sample would help, and propose a better follow-up. Unit 1
- Question 3 · 4 points Comparing two arcade players' scores Find each player's expected score, then use independence to work out probabilities for differences in their scores and the chance one player beats the other. Unit 2
- Question 4 · 4 points Seawater temperature and device reliability Plot the share of working devices against water temperature, describe the trend, and estimate the share at 40 degrees with its standard error. Unit 5, Unit 3
- Question 5 · 4 points Where moose are found near a burn Test whether moose sightings across four habitat types match the acreage proportions, then say which habitats the moose seem to favor. Unit 3
- Question 6 · Investigative Task, no longer on the exam · 4 points Magnet school test score gains Test whether magnet school students gained more than students who lost the lottery, then interpret two regression lines, read slope test results, and say what the regressions add. Unit 4, Unit 5
2008, Form B
This exam had six free-response questions, each scored from 0 to 4. Its Question 6, the Investigative Task, is no longer part of the exam. The current exam has 4 free-response questions in 90 minutes. The skills these questions practice still count.
- Question 1 · 4 points Student-to-teacher ratios at top and bottom schools Make dotplots of student-to-teacher ratios for the highest and lowest scoring schools and compare them, then explain why a test of means makes no sense here. Unit 1
- Question 2 · 4 points Choosing among four estimators Use simulated distributions of four statistics to say which are unbiased and which of each pair is the better estimator. Unit 3
- Question 3 · 4 points Budget for a brake stopping study Find whether the budget covers the sample size needed to estimate a mean within 2 feet at 95 percent confidence, and discuss what the agency's rule means for the study. Unit 4
- Question 4 · 4 points Music and blood pressure experiment Design an experiment comparing music with quiet sitting, then describe both error types and their consequences and judge which is worse. Unit 1, Unit 3
- Question 5 · 4 points Two trains meeting on a single track Find the distribution of the difference in two independent normal travel times, the long-run share of days one train waits, and the delay that cuts that chance to 0.01. Unit 2
- Question 6 · Investigative Task, no longer on the exam · 4 points Nerve swelling in Morton's neuroma Explain the clusters in two scatterplots of foot swelling, test for a mean difference between dominant and nondominant feet, and propose a swelling cutoff for diagnosis supported by a graph. Unit 5, Unit 4
2007
This exam had six free-response questions, each scored from 0 to 4. Its Question 6, the Investigative Task, is no longer part of the exam. The current exam has 4 free-response questions in 90 minutes. The skills these questions practice still count.
- Question 1 · 4 points Preservative and strawberry discoloration Explain what a standard deviation says about the control group, compare dotplots for the two groups, and use a given confidence interval to judge whether the means differ. Unit 1, Unit 4
- Question 2 · 4 points Joint supplements for older dogs Give a reason to add a control group, describe random assignment to three groups, and explain how to choose between two possible blocking variables. Unit 1
- Question 3 · 4 points Fish lengths in a stocked lake Decide which sample size makes a large sample mean more likely, compute a normal probability for a sample mean, and say whether that still works for a nonnormal population. Unit 2, Unit 4
- Question 4 · 4 points Two methods for measuring E. coli Decide, with a statistical test, whether two measuring methods applied to the same ten beef specimens give different mean readings. Unit 4
- Question 5 · 4 points Cell phones and missed freeway exits Classify the study, state hypotheses, check the conditions for a two-sample z test, and explain a given p-value and the conclusion it supports. Unit 1, Unit 3
- Question 6 · 4 points Judging distance in a dim room Interpret a regression slope, explain why a line through the origin might be preferred, test whether people overestimate distance, and sketch and interpret a model that adds a contact lens indicator. Unit 5
2007, Form B
This exam had six free-response questions, each scored from 0 to 4. Its Question 6, the Investigative Task, is no longer part of the exam. The current exam has 4 free-response questions in 90 minutes. The skills these questions practice still count.
- Question 1 · 4 points Economics test scores in a stemplot Make a stemplot of 20 test scores, describe the distribution, and explain why a measure of center alone would mislead. Unit 1
- Question 2 · 4 points Pets per household and a local law Find the chance a household breaks a pet limit, the binomial chance exactly 2 of 10 do, and describe the sampling distribution of a mean for 150 households. Unit 2
- Question 3 · 4 points Blocking windows in a test house Group the window boxes of a house into sensible blocks and justify them, then explain how to randomly assign two window types within the blocks. Unit 1
- Question 4 · 4 points Daughters' and fathers' heights Draw a given regression line on a scatterplot, show and compute one residual, and predict how adding an extreme point would change the slope and correlation. Unit 5
- Question 5 · 4 points New versus standard cholesterol drug Decide, with appropriate statistical evidence, whether a new drug lowers mean cholesterol more than the standard one in a randomized study. Unit 4
- Question 6 · 4 points Island size and bird extinction Test whether extinction rates are lower on large islands, build an interval for a regression slope on log area, use it to question an equal-rate assumption, and recommend a preserve plan. Unit 3, Unit 5
2006
This exam had six free-response questions, each scored from 0 to 4. Its Question 6, the Investigative Task, is no longer part of the exam. The current exam has 4 free-response questions in 90 minutes. The skills these questions practice still count.
- Question 1 · 4 points Comparing two toy catapults Compare dotplots of launch distances for two catapults, pick the one more likely to land in the prize band, and decide where to place it. Unit 1
- Question 2 · 4 points Detergent amount and suds height Write a regression equation from computer output, interpret the value of s, and find the slope's standard error and say what it means. Unit 5
- Question 3 · 4 points Errors in seismic depth measurements Find the chance one depth reading comes out negative, the chance at least one of three does, and the chance their mean is negative. Unit 2
- Question 4 · 4 points Emergency room wait times by arrival mode Build a 99 percent confidence interval for the difference in mean wait times and use it to judge whether the difference is significant. Unit 4
- Question 5 · 4 points Nutrients and salinity for shrimp growth List the treatment combinations, describe a completely randomized design across 12 tanks, and give one advantage and one drawback of using a single shrimp species. Unit 1
- Question 6 · 4 points Testing whether thermostat readings got less consistent State hypotheses about a variance, compute and use a chi-square statistic to test them, mark the rejection region, and use simulated histograms to rank three populations by variance. Unit 3, Unit 2
2006, Form B
This exam had six free-response questions, each scored from 0 to 4. Its Question 6, the Investigative Task, is no longer part of the exam. The current exam has 4 free-response questions in 90 minutes. The skills these questions practice still count.
- Question 1 · 4 points Real estate sales on a cumulative frequency plot Read a cumulative relative frequency graph of agents' monthly sales to explain a marked point, find the share of agents in a sales range, explain a flat stretch, and find the cutoff for the top 20 percent. Unit 1
- Question 2 · 4 points Day and night shift parts meeting specifications Build a 96 percent confidence interval for the difference in two shifts' proportions of parts within specifications, then use only that interval to judge whether the difference is significant. Unit 3
- Question 3 · 4 points Golf ball distances under a normal model Use a normal model of ball distances to find the chance one ball goes too far, the chance at least one of five does, and the largest mean that keeps 99 percent of balls under the limit. Unit 2
- Question 4 · 4 points Dexterity before and after a training program Decide with a paired test whether mean dexterity scores rose for people who finished a six week program, using before and after scores for 12 people. Unit 4
- Question 5 · 4 points Plow hitch draft experiment Name the response, treatments and units in a two plot plowing study, judge whether randomization and replication were used well, and explain why plot of land is confounded with hitch type. Unit 1
- Question 6 · 4 points Juice taste test with eight consumers State hypotheses about juice preference, explain why a large sample z test does not fit eight people, build the binomial distribution of the count, decide whether a 0.05 level is reachable, run the test, and suggest a better follow-up study. Unit 3, Unit 2, Unit 1
2005
This exam had six free-response questions, each scored from 0 to 4. Its Question 6, the Investigative Task, is no longer part of the exam. The current exam has 4 free-response questions in 90 minutes. The skills these questions practice still count.
- Question 1 · 4 points Rural and urban caloric intake stemplot Compare two distributions of calories per kilogram in a back-to-back stemplot, judge whether results from one school each generalize nationally, and pick the better of two recording plans. Unit 1
- Question 2 · 4 points Phone lines in use at a help center Find the expected value of a discrete random variable, predict how a much larger sample mean compares with a small one, find the median of the distribution, and relate mean and median to its shape. Unit 2, Unit 1
- Question 3 · 4 points Train fuel use versus number of railcars Use a scatterplot, residual plot and regression output to judge a linear model, turn the slope into a cost estimate per added railcar, interpret r squared, and judge extrapolating to 65 railcars. Unit 5
- Question 4 · 4 points Cereal box vouchers below 20 percent Test whether the proportion of cereal boxes holding a voucher is less than the company's claimed 20 percent, using 11 vouchers found in 65 boxes. Unit 3
- Question 5 · 4 points Telephone survey of high school diplomas Name a source of bias in a random digit dialing survey, find the sample size for a 0.03 margin of error at 95 percent, and describe a stratified plan that gives state estimates. Unit 1, Unit 3
- Question 6 · 4 points Lead on children's hands inside and outside Build and interpret an interval estimate of how much mean lead differs after inside versus outside play at urban centers, plot the four group means, and draw conclusions about setting, environment and their interaction. Unit 4, Unit 1
2005, Form B
This exam had six free-response questions, each scored from 0 to 4. Its Question 6, the Investigative Task, is no longer part of the exam. The current exam has 4 free-response questions in 90 minutes. The skills these questions practice still count.
- Question 1 · 4 points Shape and center of exam scores Describe the shape of 32 exam scores in a stemplot, choose whether the mean or median makes the class look better, and compute the midrange and decide what it measures. Unit 1
- Question 2 · 4 points Concert ticket purchases as random variables Find the mean and standard deviation of how many child tickets are bought, then of the total tickets and of the total amount spent when child and adult purchases are independent. Unit 2
- Question 3 · 4 points Mosquito repellent experiment designs Describe how to randomize and what inference to use for a completely randomized design and for a matched pairs design comparing two repellents, then argue which design is better. Unit 1, Unit 4
- Question 4 · 4 points Tomato seed additive paired experiment Build and interpret an interval estimate of the average growth gap between treated and untreated seeds in the same container, then use it to judge whether the difference is significant. Unit 4
- Question 5 · 4 points Walking speed and pulse rate regression Write the fitted line from regression output, decide whether the slope and intercept have sensible meanings in context, and find a margin of error for a 98 percent interval for the slope. Unit 5
- Question 6 · 4 points Milk container fill compliance Test whether a plant's mean fill is below the labeled 128 ounces, find normal probabilities for one container and for the minimum of 12, and estimate that probability from a simulation of minimums. Unit 4, Unit 2
2004
This exam had six free-response questions, each scored from 0 to 4. Its Question 6, the Investigative Task, is no longer part of the exam. The current exam has 4 free-response questions in 90 minutes. The skills these questions practice still count.
- Question 1 · 4 points Gasoline additives compared with boxplots Draw parallel boxplots of mileage changes for two additives, then pick the better additive when the goal is the most cars helped and when the goal is the largest mean gain. Unit 1
- Question 2 · 4 points Shampoo experiment with blocks of two Form six blocks of two volunteers by age, then by age and gender, and judge whether assigning whole blocks to one formula is a sound way to give out treatments. Unit 1
- Question 3 · 4 points Brontosaur femurs sampled without replacement Explain why the count of males in a sample of four bones is not binomial, find the chance all four are male, judge whether the sexes were evenly split, and decide whether the result generalizes. Unit 2, Unit 1
- Question 4 · 4 points Two antibiotic treatment plans Find the cure probability and the expected cost for two plans that try one antibiotic and then the other, and recommend a plan. Unit 2
- Question 5 · 4 points Hospital satisfaction by gender Run a chi-square test of association between gender and satisfaction from a two-way table, and judge whether the sample proportion satisfied is a fair estimate for all residents. Unit 3
- Question 6 · 4 points Cholesterol drug interval and one-sided bound Build and interpret a confidence interval for mean cholesterol reduction, explain why it disagrees with a one-sided test, then find the critical value and lower bound for a one-sided interval and compare conclusions. Unit 4
2004, Form B
This exam had six free-response questions, each scored from 0 to 4. Its Question 6, the Investigative Task, is no longer part of the exam. The current exam has 4 free-response questions in 90 minutes. The skills these questions practice still count.
- Question 1 · 4 points Moon crater age and impact rate Describe a curved relationship in a scatterplot, then interpret r squared and judge a linear fit for the log of rate against the log of age using output and a residual plot. Unit 5
- Question 2 · 4 points Dining hall food survey bias Explain how a convenience sample of the first 100 students and a leading question could each bias a survey, and suggest a fix for each. Unit 1
- Question 3 · 4 points Ore weights in hopper cars Find the normal probability that one car or the mean of 10 cars reaches 70.7 tons, and use each result to judge whether the loader is overfilling. Unit 2, Unit 4, Unit 3
- Question 4 · 4 points Homework time by grade level Build and interpret a confidence interval for the difference in mean homework time between two grades, and judge whether pairing students by rank would be a better method. Unit 4
- Question 5 · 4 points Thai dog and jackal jaw lengths Draw parallel boxplots of two samples and compare them, then judge whether a one-sample interval for the mean and a two-sample t test are reasonable for these data. Unit 1, Unit 4
- Question 6 · 4 points Banded birds on two islands Test for a difference in the proportion of banded birds on two islands, estimate one island's population from the banded share, and give two concerns about treating the captures as random samples. Unit 3, Unit 1
2003
This exam had six free-response questions, each scored from 0 to 4. Its Question 6, the Investigative Task, is no longer part of the exam. The current exam has 4 free-response questions in 90 minutes. The skills these questions practice still count.
- Question 1 · 4 points Student and teacher watch errors Draw parallel boxplots of watch errors for students and teachers, decide which group is closer to the true time, and judge whether a test about the mean answers the question about individual watches. Unit 1, Unit 4
- Question 2 · 4 points Law firm deciding on a defect lawsuit Define the parameter and hypotheses for whether the defect rate among the cars is above 5 percent, and describe both types of error and what each would cost the firm. Unit 3
- Question 3 · 4 points Shirt sizes from normal neck sizes Use a normal model of neck sizes to find the share of men not served by the stocked sizes, shade and compute the share wearing medium, and find a binomial probability for 12 customers. Unit 2
- Question 4 · 4 points Tai chi and yoga stress study Explain a problem with letting coworkers choose their program and how random assignment fixes it, say what a control group would add, and judge whether results extend to all employees. Unit 1
- Question 5 · 4 points Opinion on foreign affairs by gender Use a two-way table of responses by gender to test whether opinion on the statement depends on gender. Unit 3
- Question 6 · 4 points Shuttle company choosing coaches or vans Use expected return lines to pick a vehicle below a break-even probability, build and interpret an interval estimate of the share of markets with strong demand, and argue for and against the president's choice. Unit 2, Unit 3
2003, Form B
This exam had six free-response questions, each scored from 0 to 4. Its Question 6, the Investigative Task, is no longer part of the exam. The current exam has 4 free-response questions in 90 minutes. The skills these questions practice still count.
- Question 1 · 4 points Study hours versus work hours outlier Use regression output with and without one point to judge its influence on the line, and explain how correcting that point would change the least-squares line. Unit 5
- Question 2 · 4 points Age and income two-way table Find a marginal and a conditional probability from a two-way table of age and income, then use them to decide whether income and age are independent in the sample. Unit 2
- Question 3 · 4 points Vitamin C and flu study Decide whether the vitamin C study is experimental or observational, and name a test with hypotheses that could support the claim that vitamin C reduces flu. Unit 1, Unit 3
- Question 4 · 4 points Coffee filter and cholesterol experiment Describe how to split 300 people into two equal groups at random, explain why a control group matters, name a suitable test, and explain why only nonsmokers were used. Unit 1, Unit 4
- Question 5 · 4 points Game show spinner probability Find the chance of three straight number spins, find expected total winnings after one more spin, and test whether the four outcomes are equally likely from 100 spins. Unit 2
- Question 6 · 4 points Illness rates by age group and gender Build and interpret a confidence interval for a proportion and its confidence level, then plan how to split a sample of 2,000 so interval widths match across groups. Unit 3, Unit 1
2002
This exam had six free-response questions, each scored from 0 to 4. Its Question 6, the Investigative Task, is no longer part of the exam. The current exam has 4 free-response questions in 90 minutes. The skills these questions practice still count.
- Question 1 · 4 points Estimates of space curvature over time Read a display of estimates with margins of error from many experiments, describe how precision changed, and judge the evidence for each of two competing theoretical values. Unit 3, Unit 1
- Question 2 · 4 points Designing a boot waterproofing experiment Lay out and explain how to carry out an experiment with 100 volunteers comparing two waterproofing methods, then decide whether the design could be double blind. Unit 1
- Question 3 · 4 points Relay team mile times Use normal models for four runners to judge whether one runner's goal time is likely, then find the mean and spread of the team total and the chance of beating a past best. Unit 2
- Question 4 · 4 points Airplane operating cost versus seats Write the least squares line from regression output, find and interpret the correlation, and decide whether the same line suits a narrower range of plane sizes. Unit 5
- Question 5 · 4 points Dream recall in early birds and night owls Write other hypothesis pairs that could test whether night owls recall more dreams, then carry out a two-sample test comparing how many dreams each group recalls on average. Unit 4, Unit 3
- Question 6 · 4 points Comedy show preference and question order Build and interpret a confidence interval for a proportion, explain the confidence level, test whether answers depend on the order the shows were named, and judge whether pooling the two surveys makes sense. Unit 3
2002, Form B
This exam had six free-response questions, each scored from 0 to 4. Its Question 6, the Investigative Task, is no longer part of the exam. The current exam has 4 free-response questions in 90 minutes. The skills these questions practice still count.
- Question 1 · 4 points Swine population and atmospheric ammonia Make a scatterplot of ammonia against swine population, interpret the correlation, decide whether the relationship looks linear, and give the percent of variation explained. Unit 5
- Question 2 · 4 points Overbooked commuter flight Use a probability distribution for how many ticket holders show up to find the chance everyone gets a seat, how many no-shows to expect, and a conditional probability. Unit 2
- Question 3 · 4 points Magnet therapy for back pain Describe an experiment testing whether magnets reduce back pain, covering treatments, random assignment and the response measured, then say how the design would change with men and women available. Unit 1
- Question 4 · 4 points Social Security reform poll Construct and interpret a 95 percent confidence interval for one response proportion and explain the confidence level, then explain why a quoted reading of the poll is misleading. Unit 3, Unit 1
- Question 5 · 4 points Obstacle course times for students and faculty Draw side by side boxplots from summary statistics, compare the spread of the two groups, and write a plain summary of how the groups did. Unit 1
- Question 6 · 4 points Number of lab classes for biology majors Test whether the average count of lab classes changed over ten years, decide whether that test answers a question about the whole distribution and run a chi-square test if not, then summarize the change with graphs. Unit 4, Unit 3
2001
This exam had six free-response questions, each scored from 0 to 4. Its Question 6, the Investigative Task, is no longer part of the exam. The current exam has 4 free-response questions in 90 minutes. The skills these questions practice still count.
- Question 1 · 4 points Outliers in yearly rainfall Explain a rule for finding outliers from summary statistics, apply it to over a century of rainfall data, and comment on a news claim about one year's total. Unit 1
- Question 2 · 4 points Choosing between two photocopiers Compare the three-year cost of two machines, one with a flat repair contract and one with a per-repair cost and a probability distribution for repairs, and recommend one. Unit 2
- Question 3 · 4 points Simulating radio station prize winners Set up a simulation with random digits for drawing coupons until the prize total reaches a set amount, then run three trials on the table and report the winners in each. Unit 2
- Question 4 · 4 points Blocking plots for fruit tree varieties Choose the better of two blocking schemes for a field beside a forest and explain the purpose of randomizing within blocks. Unit 1
- Question 5 · 4 points Active ingredient in name and generic drugs Decide what to report about the difference in active ingredient between two brands bought at the same pharmacies, backing it with a paired analysis. Unit 4
- Question 6 · 4 points Predicting who finishes a Ph.D. program Compare GPAs of completers and noncompleters with a graph, judge whether GPA and credit load are related for completers, and use both regressions to predict a new applicant's outcome. Unit 1, Unit 5
2000
This exam had six free-response questions, each scored from 0 to 4. Its Question 6, the Investigative Task, is no longer part of the exam. The current exam has 4 free-response questions in 90 minutes. The skills these questions practice still count.
- Question 1 · 4 points Comparing two pain relievers by dose Use a scatterplot of average pain relief against dose to describe how each drug responds to strength and choose a drug and dose that reaches a target relief level. Unit 5, Unit 1
- Question 2 · 4 points Footprints in a prehistoric cave State the conditions needed for a t interval for mean foot length and check each one using the summary statistics given. Unit 4, Unit 1
- Question 3 · 4 points Flexibility of middle-aged and young men Make a graph from frequency tables that compares two groups' flexibility ratings, then compare the distributions in words. Unit 1
- Question 4 · 4 points Baby walkers and mental skills Test whether mean mental skill scores differ between babies who used walkers and those who did not, then explain whether a significant result would show cause. Unit 4, Unit 1
- Question 5 · 4 points Comparing two cholesterol drugs Explain a completely randomized experiment comparing two drugs, improve it with blocking, and decide whether the blocked design can be double blind. Unit 1
- Question 6 · 4 points Heights of husbands and wives Build and interpret an interval estimate of the share of couples where the wife is taller, find that chance for randomly paired adults, use both to judge independence, and sketch the shape of a scatterplot with a given correlation. Unit 3, Unit 2, Unit 5
1999
This exam had six free-response questions, each scored from 0 to 4. Its Question 6, the Investigative Task, is no longer part of the exam. The current exam has 4 free-response questions in 90 minutes. The skills these questions practice still count.
- Question 1 · 4 points Commercial aircraft counts by year Use a residual plot and regression output to judge a linear model, interpret the slope and intercept, predict one year's count, and recover the actual count from its residual. Unit 5
- Question 2 · 4 points Lost hikers and experience level Decide whether there is an association between hiking experience and the direction a lost hiker would go, backing the answer with a chi-square analysis. Unit 3
- Question 3 · 4 points Apples and dental cavities Explain why a study of apple eaters' cavities is observational, describe confounding with an example, and judge whether a significant difference shows that apples cause fewer cavities. Unit 1
- Question 4 · 4 points Quality control plans for battery weights Find the proportion of batteries each of two rejection rules would reject under a normal model, and the chance at least one of two batteries is rejected. Unit 2, Unit 1
- Question 5 · 4 points Choosing a die and a fair payoff Decide which of two unusual dice gives the better chance to win, then find the payoff that would make the game fair. Unit 2
- Question 6 · 4 points Training to predict coin tosses Test whether people beat chance after training, decide whether that test shows the training worked and run a paired analysis if not, and judge whether before scores help predict after scores. Unit 4, Unit 5
1998
This exam had six free-response questions, each scored from 0 to 4. Its Question 6, the Investigative Task, is no longer part of the exam. The current exam has 4 free-response questions in 90 minutes. The skills these questions practice still count.
- Question 1 · 4 points Sampling distribution from a skewed population Explain how the center, spread and shape of the distribution of sample means relate to a skewed population and to sample size. Unit 4, Unit 2
- Question 2 · 4 points Daily defective item counts Turn a time plot of daily defect counts into a histogram and name something each display shows that the other hides. Unit 1
- Question 3 · 4 points Marking butterfly wings for migration Describe two ways to assign six wing marking locations to butterflies, one fixing equal counts and one assigning each at random, and explain how to analyze the arrival counts under each. Unit 1, Unit 2
- Question 4 · 4 points Weed killer strength and percent killed Write the least squares line from regression output and use the residual plot to decide whether a prediction at a given strength will be too high or too low. Unit 5
- Question 5 · 4 points Graduate student demand for campus housing Test whether more than a stated share of graduate students want campus housing, then consider whether the nonrespondents could have changed the recommendation. Unit 3, Unit 1
- Question 6 · 4 points Simulating a search for pearls of the right size Find a normal probability for a pearl size, design and run a random digit simulation for opening oysters until two good pearls appear, match a simulated distribution to the scenario, and estimate the expected count. Unit 2
The questions, scoring guidelines and Chief Reader reports are College Board's. Recent years open from College Board's site and earlier years from the Internet Archive. The titles and summaries on this page are ours.