AP Statistics
Exam Review
January 2013
(Preparing for the AP Exam)AP Statistics1Topic OutlineTopicExam PercentageExploring Data20%-30%Sampling & Experimentation10%-15%Anticipating Patterns20%-30%Statistical Inference30%-40%2Exam FormatQuestionsPercent of AP GradeTime40 Multiple Choice50%90 minutes (2.25 minutes/question)6 Free-Response5 Short Answer1 Investigative Task50%90 minutes12 minutes/question
30 minutes3Free Response Question Scoring4Complete3Substantial2Developing1Minimal04AP Exam Grades5Extremely Well-Qualified4Well-Qualified3Qualified2Possibly Qualified1No Recommendation5I. Exploring DataDescribing patterns and departures from patterns (20%-30%)Exploring analysis of data makes use of graphical and numerical techniques to study patterns and departures from patterns. Emphasis should be placed on interpreting information from graphical and numerical displays and summaries.6I. Exploring DataConstructing and interpreting graphical displays of distributions of univariate data (dotplot, stemplot, histogram, cumulative frequency plot)Center and spreadClusters and gapsOutliers and other unusual featuresShape7I. Exploring DataSummarizing distributions of univariate dataMeasuring center: median, meanMeasuring spread: range, interquartile range, standard deviationMeasuring position: quartiles, percentiles, standardized scores (z-scores)Using boxplotsThe effect of changing units on summary measures8I. Exploring DataComparing distributions of univariate data (dotplots, back-to-back stemplots, parallel boxplots)Comparing center and spread: within group, between group variablesComparing clusters and gapsComparing outliers and other unusual featuresComparing shapes9
MC Example10
MC Example
MC Example2006 FR#1 The CatapultsTwo parents have each built a toy catapult for use in a game at an elementary school fair. To play the game, the students will attempt to launch Ping-Pong balls from the catapults so that the balls land within a 5-centimeter band. A target line will be drawn through the middle of the band, as shown in the figure below. All points on the target line are equidistant from the launching location. If a ball lands within the shaded band, the student will win a prize.
132006 FR#1 The CatapultsThe parents have constructed the two catapults according to slightly different plans. They want to test these catapults before building additional ones. Under identical conditions, the parents launch 40 Ping-Pong balls from each catapult and measure the distance that the ball travels before landing. Distances to the nearest centimeter are graphed in the dotplot below.
142006 FR#1 The CatapultsComment on any similarities and any differences in the two distributions of distances traveled by balls launched from catapult A and catapult B.If the parents want to maximize the probability of having the Ping-Pong balls land within the band, which one of the catapults, A or B, would be better to use than the other? Justify your choice.Using the catapult that you chose in part (b), how many centimeters from the target line should this catapult be placed? Explain why you chose this distance.15I. Exploring DataExploring bivariate dataAnalyzing patterns in scatterplotsCorrelation and linearityLeast-squares regression lineResiduals plots, outliers, and influential pointsTransformations to achieve linearity: logarithmic and power transformations16
MC Example17
MC Example18
MC ExampleCorrelation rStrength of linear association
I. Exploring DataExploring categorical dataFrequency tables and bar chartsMarginal and joint frequencies for two-way tablesConditional relative frequencies and associationComparing distributions using bar charts21
FR Example
This is an example of a Free Response question in which the first parts involve Exploratory Data Analysis and later parts involve inference.II. Sampling and ExperimentationPlanning and conducting a study (10%-15%)Data must be collected according to a well-developed plan if valid information on a conjecture is to be obtained. This includes clarifying the question and deciding upon a method of data collection and analysis.25II. Sampling and ExperimentationOverview of methods of data collectionCensusSample surveyExperimentObservational study26II. Sampling and ExperimentationPlanning and conducting surveysCharacteristics of a well-designed and well-conducted surveyPopulations, samples, and random selectionSources of bias in sampling and surveysSampling methods, including simple random sampling, stratified random sampling, and cluster sampling27
MC Example
MC Example
MC Example30II. Sampling and ExperimentationPlanning and conducting experimentsCharacteristics of a well-designed and well-conducted experimentTreatments, control groups, experimental units, random assignments, and replicationSources of bias and confounding, including placebo effect and blindingRandomized block design, including matched pairs design31
MC Example
MC Example
MC Example
MC ExampleAnticipating PatternsProbabilityInterpreting probability, including long-run relative frequency interpretationLaw of Large Numbers conceptAddition rule, multiplication rule, conditional probability, and independenceDiscrete random variables and their probability distributions, including binomial and geometricSimulation of random behavior and probability distributionsMean (expected value) and standard deviation of a random variable and linear transformation of a random variable36
MC Example
MC Example
MC ExampleProbability Sample Multiple ChoiceAll bags entering a research facility are screened. Ninety-seven percent of the bags that contain forbidden material trigger an alarm. Fifteen percent of the bags that do not contain forbidden material also trigger the alarm. If 1 out of every 1,000 bags entering the building contains forbidden material, what is the probability that a bag that triggers the alarm will actually contain forbidden material?40Organize the ProblemLabel the EventsF Bag Contains Forbidden MaterialA Bag Triggers an AlarmDetermine the Given ProbabilitiesP(A|F) = 0.97P(A|FC) = 0.15P(F) = 0.001Determine the QuestionP(F|A) ?41F0.001FC0.999ACA0.970.03Non-Conditional ProbabilitiesConditionalProbabilitiesA0.150.85ACSet up a Tree Diagram42Calculate the ProbabilityP(F|A) = P(F and A) / P(A)P(A) = P(F and A) or P(FC and A)= .001(.97) + .999(.15) = .15082P(F and A) = .001(.97) = .00097
P(F|A) = .00097/.15082 = 0.006
43III. Anticipating PatternsCombining independent random variablesNotion of independence versus dependenceMean and standard deviation for sums and differences of independent random variables
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MC Example45
MC Example
MC Example
MC Example2002 AP STATISTICS FR#3 - The Runners
There are 4 runners on the New High School team. The team is planning to participate in a race in which each runner runs a mile. The team time is the sum of the individual times for the 4 runners. Assume that the individual times of the 4 runners are all independent of each other. The individual times, in minutes, of the runners in similar races are approximately normally distributed with the following means and standard deviations.(a) Runner 3 thinks that he can run a mile in less than 4.2 minutes in the next race. Is this likely to happen? Explain.(b) The distribution of possible team times is approximately normal. What are the mean and standard deviation of this distribution?(c) Suppose the teams best time to date is 18.4 minutes. What is the probability that the team will beat its own best time in the next race?RunnerMeanSD14.90.1524.70.1634.50.1444.80.1549
