So, you’re about to take the AP Statistics Exam…
The MC SectionThere are 40 Multiple Choice questions on the exam – worth 50% of your score• Considering a 50 point possible score for the MC section:• Each MC question is worth 1.25 points• Unanswered questions do not count in the scoring calculation
There are two main types of Multiple Choice questions: Content Questions Calculation QuestionsConcept Questions These questions DO NOT deal with math. They are designed to test your knowledge of and ability to apply statistical concepts in context based questions. • Answer choices will be verbal • Little or no calculation required to answer • Very little time to answer • Usually about 10-15 questions per examCalculation Questions These questions DO involve math. They are designed to test your ability to use concept knowledge to calculate appropriate answers. • Answer choices will be number based • Knowledge of formulas, tables and/or calculator is required • These take more time to answer • Accounts for the majority of the test
A typical concept question might look like this:A simple random sample of size n is taken from a large population whose distribution ofthe variable under consideration is extremely right-skewed. Which of the followingstatements is true? A. As n increases, the sample mean is more likely to be within a given distance of the population mean. B. When n > 30, the distribution of the sample mean is normal. C. As n increases, the sample standard deviation decreases. D. As n increases, the distribution of the sample data becomes more normal. E. The sample standard deviation is equal to population standard deviation n A typical calculation question might look like this: A 95% confidence interval is to be calculated in order to find an estimate for a population proportion. What is the smallest sample size that will guarantee a margin of error of at most 5%? A. 225 B. 350 C. 400 D. 575 E. 800
How to increase your MC score:• Use your time wisely. 90 minutes for 40 questions = 2.25/?• Do not work consecutively – do what you know first • This may seem counterintuitive, but if you read the question and are confident about the solution method, go ahead and carry it out. • If a question seems tough and you are unsure about it, keep a list on your work book of the numbers you need to go back to and revisit it when you have exhausted all of the easier questions. • Remember…all MC questions carry the same value. Don’t let yourself run out of time because you spent it all on difficult questions.
The FRQ SectionThere are 6 Free Response Questions on the exam – worth 50% of your score:• 5 essay questions •These questions will represent the four main topics of Statistics •Analyzing Data •Producing Data •Probability and Random Variables •Inference •They should take about 12 minutes each •They are worth 75% of Section 2 (37.5% of the entire test)• 1 investigative task •This question will test several concepts and procedures from throughout the course in the context of a single problem. •Should take about 30 minutes •This is worth 25% of Section 2 (12.5% of the entire test)
On problems where you have to produce a graph: Label and scale your axes! Do not copy a calculator screen verbatim onto the test. Dont refer to a graph on your calculator that you havent drawn. Transfer it to the exampaper. This is part of your burden of good communication.Communicate your thinking clearly.o Organize your thoughts before you write, just as you would for an English paper.o Write neatly.o Write efficiently. Say what needs to be said, and move on. Dont ramble.o The burden of communication is on you. Dont leave it to the reader to make inferences.o Dont contradict yourself.o Parallel solutions are graded on the incorrect answer.o Avoid bringing your personal ideas and philosophical insights into your response.o When you finish writing your answer, look back. Does the answer make sense? Did youaddress the context of the problem?
About graphing calculator use: Dont waste time punching numbers into your calculator unless youre sure it is necessary. Enteringlists of numbers into a calculator can be time-consuming, and certainly doesnt represent a display ofstatistical intelligence. * Do not write directions for calculator button-pushing on the exam! * Avoid calculator syntax, such as normalcdf or 1-PropZTest.Follow directions. If a problem asks you to "explain" or "justify," then be sure to do so. * Dont "cast a wide net" by writing down everything you know, because you will be graded oneverything you write. If part of your answer is wrong, you will be penalized. * Dont give parallel solutions. Decide on the best path for your answer, and follow it through to thelogical conclusion. Providing multiple solutions to a single question is generally not to your advantage. Youwill be graded on the lesser of the two solutions. Put another way, if one of your solutions is correct andanother is incorrect, your response will be scored "incorrect."The amount of space provided on the free-response questions does not necessarily indicatehow much you should write.If you cannot get an answer to part of a question, make up a plausible answer to use in theremaining parts of the problem.
Words from the Chief AP reader (after the 2001 exam):Areas that continue to be problematic are listed below.• Many students failed to read questions carefully and, as a result answered aquestion different from the one that was asked.• Many students did not answer questions in context. Explanations andconclusions in context are always required for a complete answer.• More students than in past years stated assumptions when carrying out ahypothesis test, but few understood that assumptions must also be checked.•A large number of students seem to believe that it is okay to draw conclusionsby "just looking at the data," and did not seem to understand the need toemploy inferential procedures even when asked to provide statistical evidenceto support their conclusions.
FRQ Scoring Breakdown4 Complete Response NO statistical errors and clear communication Minor statistical error/omission or fuzzy3 Substantial Response communication Important statistical error/omission or lousy2 Developing Response communication A "glimmer" of statistical knowledge related to1 Minimal Response the problem No glimmer; statistically dangerous to himself0 Inadequate Response and others
During the ExamRelax, and take time to think! Remember that everyone else taking the exam is in asituation identical to yours. Realize that the problems will probably look considerablymore complicated than those you have encountered in other math courses. Thats becausea statistics course is, necessarily, a "wordy" course.Read each question carefully before you begin working. This is especially important forproblems with multiple parts or lengthy introductions. Suggestion: Highlight key wordsand phrases as you read the questions.Look at graphs and displays carefully. For graphs, note carefully what is represented on theaxes, and be aware of number scale. Some questions that provide tables of numbers andgraphs relating to the numbers can be answered simply by "reading" the graphs.About graphing calculator use: Your graphing calculator is meant to be a tool, to be usedsparingly on some exam questions. Your brain is meant to be your primary tool.
On multiple-choice questions: * Examine the question carefully. What statistical topic is being tested? What is thepurpose of the question? * Read carefully. Highlight key words and phrases. After deciding on an answer, glanceat the highlighted words and phrases to make sure you havent made a careless mistakeor an incorrect assumption. * Keep scoring in mind: (Number Right) minus (one-quarter)(Number Wrong). Carelessmistakes hurt. If you can eliminate more than one answer choice, you might benefit byguessing. * You dont have to answer all of the questions to get a good overall score. * If an answer choice seems "obvious," think about it. If its so obvious to you, itsprobably obvious to others, and chances are good that it is not the correct response. Forexample, suppose one set of test scores has a mean of 80, and another set of scores onthe same test has a mean of 90. If the two sets are combined, what is the mean of thecombined scores. The "obvious" answer is 85 (and will certainly appear among theanswer choices), but you, as an intelligent statistics student, realize that 85 is notnecessarily the correct response.
On free-response questions: * Do not feel pressured to work the free-response problems in a linear fashion, forexample, 1, 2, 3, 4, 5, 6. Read all of the problems before you begin. Question 1 is meant tobe straightforward, so you may want to start with it. Then move to another problem thatyou feel confident about. Whatever you do, dont run out of time before you get toQuestion 6. This Investigative Task counts almost twice as much as any other question. * Read each question carefully, sentence by sentence, and highlight key words orphrases. * Decide what statistical concept/idea is being tested. This will help you choose aproper approach to solving the problem. * You dont have to answer a free-response question in paragraph form. Sometimes anorganized set of bullet points or an algebraic process is preferable. * Answer each question in context.
Collecting DataThere are 2 broad areas of data collection we cover in AP Stat, Experiments and Sampling.You are expected to know some general concepts and specific techniques related to eacharea.Experiments vs. SamplesMany students confuse experimentation with sampling or try to incorporate ideas from oneinto the other. This is not totally off-base since some concepts appear in both areas, but it isimportant to keep them straight.The purpose of sampling is to estimate a population parameter by measuring arepresentative subset of the population. We try to create a representative sample byselecting subjects randomly using an appropriate technique.The purpose of an experiment is to demonstrate a cause and effect relationship bycontrolling extraneous factors. Experiments are rarely performed on random samplesbecause both ethics and practicality make it impossible to do so. For this reason, there isalways a concern of how far we can generalize the results of an experiment. Generalizingresults to a population unlike the subjects in the experiment is very dangerous.
Blocking vs. StratifyingStudents (and teachers) often ask, "What is the difference between blocking andstratifying?" The simple answer is that blocking is done in experiments and stratifying isdone with samples. There are similarities between the two, namely the dividing up ofsubjects before random assignment or selection, but the words are definitely notinterchangeable.BlockingIn blocking we divide our subjects up in advance based on some factor we know or believeis relevant to the study and then randomly assign treatments within each block. The keythings to remember:1. You dont just block for the heck of it. You block based on some factor that you think willimpact the response to the treatment2. The blocking is not random. The randomization occurs within each block essentiallycreating 2 or more miniature experiments.3. Blocks should be homogenous (i.e. alike) with respect to the blocking factor.For example, I want to find out if playing classical music during tests will result in higher mean scores. I couldrandomly assign half my students to the room with the music and the other half to the normal room, but I know thatmy juniors consistently score higher than my seniors, and I want to account for this source of variation in the results.I block according to grade by separating the juniors and seniors first and then randomly assigning half the juniors tothe music room and the other half to the normal room. I do the same with the seniors. For this design to be valid, Ihave to expect that each grade will respond to the music similarly. In other words, I know that juniors will scorehigher, but I expect to see a similar improvement or decline in both groups as a result of having the music. At theend of my study I can subtract out the effect of grade level to reduce the unaccounted for variation in the results.
Stratified Sampling vs. Cluster SamplingMany students confuse stratified and cluster sampling since both of them involve groups ofsubjects.There are 2 key differences between them. First, in stratified sampling we divide up thepopulation based on some factor we believe is important, but in cluster sampling thegroups are naturally occurring (I picture schools of fish). Second, in stratified sampling werandomly select subjects from each stratum, but in cluster sampling we randomly selectone or more clusters and measure every subject in each selected cluster. (Note: There aremore advanced techniques in which samples are taken within the cluster(s))Final ThoughtsIt is especially important to stay focused when answering questions about design. Toomany students get caught up in minor details but miss the big ideas of randomization andcontrol. Always remember that your mission in responding to questions is to demonstrateyour understanding of the major concepts of the course.
Describing DataIQR is a numberMany students write things like "The IQR goes from 15 to32". Every AP grader knowsexactly what you mean, namely, "The box in my boxplot goes from 15 to 32.", but thisstatement is not correct. The IQR is defined a Q3 - Q1 which gives a single value. Writingthe statement above is like saying "17 goes from 15 to 32." It just doesnt make sense.Be able to construct graphs by handYou may be asked to draw boxplots (including outliers), stemplots, histograms, or othergraphs by hand. The test writers have become very clever and present problems in such away that you cannot depend on your calculator to graph for you.Label, Label, LabelAny graph you are asked to draw should have clearly labeled axes with appropriate scales.If you are asked to draw side-by-side boxplots, be sure to label which boxplot is which.
Refer to graphs explicitlyWhen answering questions based on a graph(s), you need to be specific. Don_t just say,"The female times are clearly higher than the male times.", instead say, "The median femaletime is higher than the first quartile of the male times." You can back up your statements bymarking on the graph. The graders look at everything you write, and, often, marks on thegraph make the difference between 2 scores.Look at all aspects of dataWhen given a set of data or summaries of data, be sure to consider the Center, Spread,Shape, and Outliers/Unusual Features. Often a question will focus on one or two to theseareas. Be sure to focus your answer to match.Its skewed which way?A distribution is skewed in the direction that the tail goes, not in the direction where thepeak is. This sounds backwards to most people, so be careful.Slow downThe describing data questions appear easy, so many students dive in and start answeringwithout making sure they know what the problem is about. Make sure you know whatvariable(s) are being measured and read the labels on graphs carefully. You may be givena type of graph that you have never seen before
InferenceNot every problem involves inferenceYou have spent most if not all of this semester on inference procedures. This leads manystudents to try to make every problem an inference problem. Be careful not to turnstraightforward probability or normal distribution questions into full-blown hypothesistests.Hypotheses are about populationsThe point of a hypothesis test is to reach a conclusion about a population based on asample from it. We dont need to make hypotheses about the sample. When writinghypotheses, conclusions, and formulas, be careful with your wording and symbols so thatyou do not get the population and sample mixed up. For example, dont write "Ho: x = 12"or "µ = mean heart rate of study participants".Check Assumptions/ConditionsChecking assumptions/conditions is not the same thing as stating them. Checking meansactually showing that the assumptions are met by the information given in the problem.For example, dont just write "np>10". Write "np=150(.32)=48>10". Everyone knows youcan do the math in your head or on your calculator, but writing it down makes it very clearto the reader that youre tying the assumption to the problem rather than just writing alist of things you memorized.
Confidence intervals have assumptions tooConfidence intervals have the same assumptions as their matching tests, andyou need to check them just as carefully.Link conclusions to your numbersDont just say "I reject Ho and conclude that the mean heart rate for males isgreater than 78." This sentence doesnt tell us why you rejected Ho. Instead, say"Since the p-value of .0034 is less than .05, I reject Ho and ...”Be consistentMake sure your hypotheses and conclusion match. If you find an error in yourcomputations, change your conclusion if necessary. Even if your numbers arewrong, you will normally get credit for a conclusion that is correct for yournumbers. If you get totally stuck and cant come up with a test statistic or p-value, make them up and say what you would conclude from them.
Interpreting a confidence interval is different than interpreting theconfidence levelInterpreting the confidence interval usually goes something like, "I am 95%confident that the proportion of AP Statistics students who are highlyintelligent is between 88% and 93%" or "The superintendent should giveseniors Fridays off since we are 99% confident that between 72% and 81% ofparents support this plan.“Interpreting a confidence level usually goes something like "If this procedurewere repeated many times, approximately 95% of the intervals producedwould contain the true proportion of parents who support the plan."
RegressionGraph First, Calculate LaterThe most important part of the regression process is looking at plots. Regressionquestions will frequently provide a scatterplot of the original data along with aplot of residuals from a linear regression. Look at these plots before answeringany part of the question and make sure you understand the scales used.Is it linear?Remember that an r value is only useful for data we have already decided is linear.Therefore, an r value does not help you decide if data is linear. To determine ifdata is linear, look at a scatterplot of the original data and the residuals from alinear regression. If a line is an appropriate model, the residuals should appear tobe randomly scattered.
Computer OutputIt is very likely that you will be given computer output for a linearregression. If you can read the output correctly, these questions arenormally easy. You should be able to write the regression equation using thecoefficients in the output and also be able to find the values of r and r^2.Most software packages provide the value of r^2.If you are asked for the value of r, you will need to take the square root andlook at the slope to determine if r should be positive or negative.Interpreting rIf asked to interpret an r value, be sure to include strength, direction, type,and the context. A good interpretation will be something like, “There is aweak positive linear relationship between the number of math classes aperson has taken and yearly income.”