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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	Cholesterol Experimental design; blocking; double-blinding
6 (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	Husband-and-Wife 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	Lawsuits 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	Skunk! 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
4	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
6 (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 SE_b	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
6 (Inv. Task)	Thermostats 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
6 (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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College Board

AP Central

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

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

See also...

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

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