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Home > AP Statistics Exam Questions -- Free-Response Question Analysis for 1997 to 2008

AP Statistics Exam Questions -- Free-Response Question Analysis for 1997 to 2008

by Daren Starnes
The Lawrenceville School
Lawrenceville, New Jersey

Question 1997 1998 1999 2000
1 1900 vs. 2000 population
Cumulative distribution (ogives), medians, IQR Comparing distributions
CLT means what?
Sampling distribution of sample mean; CLT
Lydia & Bob - air travel
Linear regression; slope and y-intercept; residuals
Drug A and Drug B
Scatterplots; graphical interpretation
2 Fish tank
Experimental design; blocking
Defective items
Scatterplot vs. histogram; graphical interpretation
Lost hikers
Chi-square test of association
Cave & Footprints
Assumptions for inference about means
3 Drug testing
Probability (tree); conditional probability
Butterfly tagging
Randomization; analyzing data
Dentists and apples
Observational study vs. experiment; confounding; establishing causation
Male flexibility
Constructing graphs for tabular data; graphical interpretation and comparison
4 Political candidate
Two proportion inference; significance test (1-tailed)
Weed killer
Linear regression; Computer printout; residual plots
Defective batteries
Normal calculations; IQR; probability calculation
Baby Walkers
Two sample inference for means; two-tailed; causation?
5 Oven chips
matched pairs vs. two sample;Two-tailed procedure
Graduate housing
One proportion inference; significance test (1-tailed)
Die A and Die B
Probability; expected value
Experimental design; blocking; double-blinding
(Inv. Task)
Auto depreciation
Linear and nonlinear regression models; computer printouts
Oysters and pearls
Normal calculations; Simulation; expected value
Guessing coin tosses
One proportion inference; matched pairs; correlation
Normal calculations; diff of 2 rand var's; independence; the ellipse

Question 2001 2002 2002 Form B 2003 2003 Form B
1 L. A. Rainfall
Outliers, summary statistics, exploratory data analysis
Einstein vs. Newton
Graphical interpretation; interpreting CI's
Swine & Ammonia
Scatterplots, correlation, r-squared
Accurate watches
Parallel boxplots, graphical interpretation, choosing inference procedure
Studying & work
Computer regression output; influential points
2 Copier Repairs
Random variables & expected value
Give me the boot!
Matched pairs design; double blind
Airline no-shows
Expected value; probability; conditional probability
One proportion hypothesis and parameter; Type I, II error
Age & Income survey
Tabular probability; conditional probability; independence
3 Radio Giveaway
Designing and performing a simulation
Fast runners
Normal calculation Combining r.v.'s - means & variances
Magnet therapy
Comparative, randomized expt; blocking
Men's shirt sizes
Normal distributions, binomial probability
Vitamin C & flu
Experiment vs. observational study; Choosing inference procedure
4 Dwarf fruit trees
Blocking & randomization
Airline costs
Linear regression; computer printout; correlation
Social security
One-proportion CI & Interpreting categorical data
Tai chi and yoga
Random assignment, control group, generalizability
Coffee & cholesterol
Random assignment; control group; choosing inference procedure; lurking variables
5 Name brand vs. generic drugs
Matched pairs t-procedures
Owls & early birds
Stating hypotheses; two-sample t-test
Obstacle course
Parallel boxplots; comparing center & variability
Presidential survey
Chi-square test of independence
Probability; expected value; chi-square goodness-of-fit test
6 Predicting Ph.D. from GPA
Comparative displays; inference for regression slope; LSRL and prediction
S or F?
One proportion CI; interpreting confidence; two proportion z-test or chi-square test
Lab classes
Two sample t-test Chi-square GOF test Bar graphs
Shuttle bus!
Graphical interpretation, one proportion CI, interpreting CIs, probability
HMO study
One-proportion CI; interpret 95% confident; adjusting MOE (determining sample size)

Question 2004 2004 Form B 2005 2005 Form B
1 Gasoline additives
Parallel boxplots, outliers; comparing proportions and means
Craters on the moon
Describe scatterplot;
log transformation;
residual plot; interpreting r2
Adolescent calories
Back-to-back stemplot; interpreting graphs; generalizability; study design
Exam scores
Stemplot; describing graphs; mean vs. median; midrange
2 New Shampoo
Blocking by one/ two factors;
Random assign. of treatments
Dining hall food
Bias of sampling method; bias of question wording
Telephone lines
Expected value of r.v.; sampling distr. of sample mean; mean vs. median; shape
Concert tickets
Mean and std. dev of r.v.; Combining r.v.'s - mean and std. dev
3 Brontosaur bones
Binomial conditions; conditional probability; generalizability;
interpreting probability
Trains filled with ore
Normal calculation; probability interpretation; Sampling distr of sample mean
Train fuel consumption
Appropriateness of linear model; predicting with LSRL; interpreting r2; extrapolation
Mosquito repellent
Completely randomized design; matched pairs design; randomization method

Antibiotics for ear infections
Probability (tree diagram), expected value; interpretation

Homework in middle school
Two-sample t interval; matched pairs vs. two samples

Cereal box vouchers
One-proportion z test (one-sided)
Tomato seeds
Matched-pairs t interval; performing significance test using CI
5 Satisfaction with hospital
Chi-square test of assoc/indep; generalizability
Thai dogs and golden jackals
Parallel boxplots;
Conditions for one-sample t; Conditions for 2-sample t
Educational level survey
Survey bias and effect; determining sample size; stratified sampling
Walking speed & pulse
Regression output; interpreting slope and intercept; CI for slope
(Inv. Task)
New cholesterol drug
One-sample t interval;
CI vs significance test;
one-sided CI; interpretation
Banded birds
Two-proportion z test or chi-square test of homogeneity; capture-recapture; assumptions
Get the lead out!
Two-sample t interval; interaction effects
Not enough milk?
One-sample t test; normal calculation; sampling distr. of sample mean; simulation


Question 2006 2006 Form B 2007 2007 Form B
1 Comparing Catapults
Parallel dotplots; comparing shape, center, and spread; interpreting center, variability
Real estate agents
Interpreting a cumulative relative frequency graph
Preserving strawberries
Interpret standard deviation; interpreting comparative dotplot; interpreting two-sample t interval
Kids not learning econ
Constructing a stemplot; describing distributions: shape, center, spread, outliers
2 Suds
Computer output; equation of LSRL; interpreting s; interpreting SEb
Day shift vs. night shift
96% CI for p1-p2 ; connecting CI to significance test
Aging dogs
Purpose of control group; describing random assignment; blocking
How many dogs and cats?
Random variables & probability;
binomial probability; sampling distribution of sample mean
3 Deep beneath the Earth
Normal calculations; probability calculation; calculation involving sampling distribution of sample mean

Golf balls & Iron Byron
Normal calculations; probability calculation; inverse normal calculation

Big Town Fisheries
Sampling distribution of sample mean; Normal probability calc.; central limit theorem
Energy efficient windows
Blocking; implementing random assignment
4 Ambulance or drive yourself
Two-sample t CI; connecting CI to significance test
Improving dexterity
Paired t test

E. coli in beef
Paired t procedures:
two-tailed test or CI

Women’s & Father’s heights
Plotting the LSRL; determining a residual; influence of a point on slope and correlation

5 Tiger shrimps
Two-factor experiment; treatments; completely randomized design; reducing variability; generalizability
Plowing the fields
Response variable; treatments; experimental units; randomization; replication; confounding
Distracted driving
Experiment vs. obs. study; stating hypotheses;
verifying conditions; interpreting P-value
Lowering serum cholesterol
Two-sample t test
(Inv. Task)
Significance test about σ2: stating hypotheses; calculating test statistic and P-value; drawing conclusions; simulated sampling distributions
Sunshine Farms Juice
Stating hypotheses; conditions for one-proportion z test; binomial probability; significance level; carrying out binomial test; increasing power
Judging distances
Interpreting slope; implication of y-intercept in model; significance test of  H0: ß=1 interpreting the effect of adding an indicator variable to linear model
Preserving bird species
Two-proportion z test; CI for regression slope; transformation using logs; examining independence; making decisions based on predictions


Question 2008 2008 Form B
1 Sugary cereal
Parallel boxplots; comparing shape, center, and spread; changing units of measurement; mean vs. median
Student-teacher ratio
Construct and interpret dotplots; comparing distributions; why inference isn't appropriate
2 School board surveyNonresponse bias; larger samples not always better
Nonresponse bias; larger samples not always better
Good estimators
Unbiased estimators;
what makes an estimator good?
3 Arcade game
Mean of discrete r.v.; probability rules: addition, multiplication, complement
Braking distance
Determining sample size for specified margin of error; interpreting consequences
4 Temperature and reliability
Making and interpreting scatterplot; standard error of estimate
Music and blood pressure
Completely randomized design; Type I and II errors and consequences
5 Moose
Chi-square test for goodness of fit; contributions of individual cells
Snake gulch railroad
Combining normal random variables;
calculating normal probabilities and
inverse normal values
(Inv. Task)
Magnet schools
Two-sample t test; computer output; interpreting slope of LSRL in context; test for correlation/slope of LSRL
Morton's neuroma
Interpreting scatterplots; Paired t test; Developing diagnostic criteria

Daren Starnes is Master Teacher in Mathematics at The Lawrenceville School near Princeton, NJ. Since 1998, he has been a reader, table leader, and question leader for the AP* Statistics exam. Daren has served on the ASA/NCTM Joint Committee on Curriculum in Statistics and Probability since 2004.

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