AP Statistics Exam Tips Many thanks to many colleagues for tips Lew Davidson (Dr. D.) Mallard Creek High School

For an electronic copy of this presentation, please me: Quick questions – call me at home

KNOW YOUR EXAM! 12 Years - Questions & Answers rse/ap-statistics/exam-practice Or go to AP (2 nd Item, top menu bar) Get Practice Questions (1 st row, right blue box) Scroll down to AP Statistics 3

Get Familiar with Exam Format Look at 2012 Exam - (link on previous slide) Pages 3 – 5: (both MC and FR) Formulas - understand them! Pages 14 – 17: (both MC and FR) Tables - understand them! What do they mean? How do we use them? 4

The Multiple Choice Section WARNING: These comments are based on Dr. D.’s views and are not guarantees. They are “food for thought” to help in making your decision on how to take the exam. Be aware some “gurus” (I am not at that level) suggest other approaches. In the end you must decide what is right for you - it is your test! 5

Multiple Choice [90 minutes – 40 questions] Answer every question. (period!!!!!!!) Do work in the test book and circle answers there – but remember work/answers in the test book are neither graded nor seen! Only the bubble sheet is graded–That’s It Only bubble when you are done [Dr. D.’s view] – but leave time to bubble! TRY to NOT ERASE on the bubble sheet! 6

Answering Multiple Choice Questions Know your test – For AP Statistics –No penalties for wrong answers (Answer every one) –One or two questions may make a huge difference in your normalized score! (Your score is based on relative performance) - EVERY ONE QUESTION COUNTS BIG TIME –Bubble BEST ANSWER in the context of the question Possible: No answer choice may be precisely correct or Possible: More than one choice may be correct 7

Answering Multiple Choice Questions Know your test – For AP Statistics –Often the stem has extraneous information –Often data is given, but there may also be a summary metric which precludes the need for calculations –No Highlighting BUT YOU CAN WRITE IN THE TEST BOOK –Bubble Sheet: Weakly erased answers or stray marks may result in wrong scanned scores – and no one will know it!  That is why you need a super eraser! 8

Multiple Choice Questions Cover answer choices (called distracters!): –Do not start calculations until you understand the question –Read (skim if long) the stem of the question –Underline the precise question (usually at the end) [note: Highlighters are not allowed] –Think about the intent of the question (what content is the author trying to find out if you understand) –Reread the stem -- thinking about the precise question and intent –Determine the most likely answer(s) 9

Multiple Choice Example # 2 Page 20 of College Board’s Course Description Under which of the following conditions is it preferable to use stratified random sampling rather than simple random sampling? The population can be divided into: (a) a large number of strata so that each stratum contains only a few individuals (b) a small number of strata so that each stratum contains a large number of individuals (c) strata so that the individuals in each stratum are as much alike as possible (d) strata so that the individuals in each stratum are as different as possible (e) strata of equal sizes so that each individual in the population still has the same chance of being selected 10

Multiple Choice Example #2 Page 20 of College Board’s Course Description Under which of the following conditions is it preferable to use stratified random sampling rather than simple random sampling? 11

Multiple Choice Example # 2 Page 20 of College Board’s Course Description Under which of the following conditions is it preferable to use stratified random sampling rather than simple random sampling? So we need to know what are these 2 types of sampling and how are they different when it is best to use one or the other 12

Multiple Choice Example Page 20 of College Board’s Course Description Under which of the following conditions is it preferable to use stratified random sampling rather than simple random sampling? The population can be divided into [a]: (a) large number of strata so that each stratum contains only a few individuals (b) small number of strata so that each stratum contains a large number of individuals (c) strata so that the individuals in each stratum are as much alike as possible (d) strata so that the individuals in each stratum are as different as possible (e) strata of equal sizes so that each individual in the population still has the same chance of being selected 13

Multiple Choice Questions Compare your answer(s) to the answer choices Look at each answer choice & mark off those that are clearly impossible choices Watch out for answers that are part of your solution calculations/considerations but do not answer the precise question If you are sure of an answer – circle it and move on --- DO NOT BUBBLE ANY ANSWERS AT THIS TIME If not sure, leave possible choices unmarked (you should designate the answer(s) that seems most likely). Mark this question (On the test only) and return to it later 14

Multiple Choice Questions Often as you are doing a test you will get an idea on an earlier problem DO NOT SPEND TOO MUCH TIME ON ONE QUESTION – figure your pace and more on! – for the AP Exam there are 90 minutes for 40 questions –So MOVE ON if a question is not answered in 2 minutes I understand many kids finish a first pass of the MC test in one hour or so. Thus you probably will have time to go back. (Dr.D.’s view) Do not bubble at this stage to minimize eraser errors BUBBLE in the last 10 minutes (WATCH YOUR TIME). 15

Multiple Choice Questions #4 (Dr.D.’s view) DO not pass in your test early – CHECK YOUR ANSWERS If GUESSING go with your first guess. Only change your first guess if you think of a specific reason to change it Use a MARS or equivalent eraser Do not OVERANALYZE the problem. Think of the Intent and go for the BEST not necessarily the PERFECT answer 16

See College Board Resource Go to the Course Description link on the College Board link on Slide # 3, then select Course Description to get to: student/course/ap-statistics-2010-course- exam-description.pdf student/course/ap-statistics-2010-course- exam-description.pdf Study Multiple Choice section: Pages

The Free Response Section First, I share my viewpoints as a complement to the great resources included next from key teachers

The Free Response Section WARNING: These comments are based on Dr. D.’s views and are not guarantees. They are “food for thought” to help in making your decision on how to take the exam. Be aware some “gurus” (I am not at that level) suggest other approaches. In the end you must decide what is right for you - it is your test! 19

Free Response Questions Must move fast & write only what is needed - most kids report not enough time 1 st : Five comprehensive questions (75%) They usually include different parts of our course 1 st Question: Plan ≤ 10 minutes (often Descriptive) Next four: average ≈ 12 minutes each 2 nd : Investigative Task (25 % of FR Score) Plan on 25 minutes – Just follow the prompts! It is best to use bullets unless sentence(s) or paragraphs are requested 20

Game Plan Many say 1 st read all questions – Dr. D. disagrees. -- “Not enough time”, I say Consider this approach 1.Do Q#1: It is usually the easiest & fastest - 10 Minutes MAXIMUM 2.Next Do Q#6 – Investigative task, unless you have no idea what to do. Usually, just follow the prompts EXACTLY 30 Minutes MAXIMUM 3.Next Do Q #2 – # 5 in order: Do or come back 4.Say what you know-you may get partial credit 21

Exam booklet Insert An insert in the exam booklet contains the questions without the answer spaces Remove it from the exam booklet and use it for reference No credit is given for anything written on the insert (readers do not see it) Write answers and all your work for each problem in the pages in the exam booklet! 22

The Plays – in EXAM Booklet 1.Glance at last sentence or a), b), etc of answer choices – get a sense of problem 2.Start reading from the beginning of the question, but for now just scan long scenario descriptions – now you understand the problem 3.Now read carefully from the start and underline the key facts you need 23

Free Response Scoring 1 st Readers check for specific attributes specified in the rubrics (0 – 4 points total) Then Readers holistically consider your demonstrated knowledge & set your score Unlike Multiple Choice: Partial Credit is granted! There are no penalties for wrong answers 24

Free Response Ideas Readers “are on your side” and record points based on work shown Write what you best know on the topic Some work can earn Partial Credit Note: Blank = zero! NO “alternate solutions”  give it your best shot! (if 2 solutions, your worst one is scored  so cross out worst comments! 25

Readers must read & understand Be legible! (Dark pencil or pen) Write in good sentences! Show a logical flow! Clearly show your work and answer! Use standard statistical jargon! The answer space provided has plenty of room for what is expected – use it as a guide for the maximum answer length Often only some of the space is needed! 26

See College Board Resource Go to the Exam Practice College Board link on Slide # 3, (see each year’s questions at bottom and select Course Description to get to: student/course/ap-statistics-2010-course- exam-description.pdf student/course/ap-statistics-2010-course- exam-description.pdf Study Free Response Questions section: Pages

Answers for FR Practice At the bottom of the College Board resource link page (Slide # 3 of this presentation) select the Free Response Questions for year 2001 Note  The question #’s for the pg questions in the course description correspond to the 2001 question numbers (Follow links to see the answers) 28

Misc – But Important You can bring two calculators to the exam You can bring extra batteries - DO IT! Bring at least two sharp # 2 Pencils Bring a super eraser! -- Note if the scanner can’t read one of your answers, you will not know it! Have “Catalog Help” on your TI 83 or 84 Know how to activate “Catalog Help” and “Diagnostics On” 29

AP Statistics Exam Tips 2012 Edition Daren Starnes The Lawrenceville School BFW Publishers May 3, 2012

#1. Get Prepared! Do released AP Exam MC and FR questions Do practice questions from other sources –Stats 4 Stem 4 Stem –AP Statistics Review books –Cumulative AP Practice Tests in TPS 4e Review Formulas and Tables for AP ExamFormulas and Tables for AP Exam Review inference procedures – ob/categorizingStatProblems12.html –Inference summary from TPS 4e endpapersInference summary 31

#2: Be a smart test taker! General –Get a good night’s sleep –Review TPS 4e Appendix A AP Exam TipsTPS 4e Appendix A AP Exam Tips –Eat a healthy lunch –Check that your calculator is working Multiple choice section –Answer all the questions (no guessing penalty) –Cover up answers while reading the stem Free response section –Don’t run out of time before Question 6!! –Start with questions you feel confident about –Use bullets and outlines rather than complete sentences whenever possible 32

#3: Use technology wisely Don’t type in data just because it’s there! On inference questions, use STAT TESTS for calculations. Only show formulas with values subbed in for partial credit if you get the same answer! Calculator speak = no full credit (1) Binompdf(12,.2,3) = no full credit Better: P(X = 3) = (12C3)(0.2) 3 (0.8) 9 Minimal: binompdf with n = 12, p =.2, k = 3 (2) Normalcdf(90,105,100,5) = no full credit Better: Find z score. Then draw, label, shade Normal curve Minimal: normalcdf with lower bound = 90, upper bound = 1- 5, mean = 100, std. dev. = 5 33

#4: Follow the 4-step inference process Starting in 2010, partial credit became available on 4-step rubrics. 34

#4: Follow the 4-step inference process Remember: Don’t just start typing in the data unless you have a reason to do so!! 2010 Question #5: Fish tales 2011 Question #4: High Cholesterol 35

#4: Follow the 4-step inference process 2011 Question #4: High Cholesterol RIN TIN TIN 36

#4: Follow the 4-step inference process 2011 Question #4: High Cholesterol 37

#4: Follow the 4-step inference process 2011 Question #4: High Cholesterol Now for Step 3: State the calculator test Report: Test Statistic p-value df (mean only) 38

#4: Follow the 4-step inference process Do not “accept” the null hypothesis!! 2011 Question #4: High Cholesterol 39

#5: Don’t shoot yourself in the foot! Misuse of term or notation  mandatory deduction –Putting statistics instead of parameters in hypotheses –Saying there’s confounding when there isn’t –Using experiment language in an observational study Blocking vs. stratified sampling; experiment vs. survey Advice: –Only use terms and symbols you know –It’s better to explain in your own words than to use a term incorrectly –If you’re unsure about notation, use words instead of symbols 40

#6: Naked answer = no credit Directions: Show all your work. Indicate clearly the methods you use, because you will be graded on the correctness of your methods as well as on the accuracy and completeness of your results and explanations. 2009, Question #2 41

#6: Naked answer = no credit 2009, Question #2(a): 70 th percentile of stopping distances 42

#7: If you can’t answer part of a question, don’t assume you can’t answer other parts If needed, make up a reasonable answer for the part you can’t answer… 2010 Question #4 43

#8: Know what distribution you’re talking about! 1.Population distribution (lengths of all rock-and-roll songs the station plays) 2.Distribution of sample data (lengths of 40 songs in the sample) 3.Sampling distribution of statistic (e.g. sample means of all song length samples) 2010 Question #2 44

#9: Don’t write too much Answer the question, then STOP ! Space provided is more than enough The mandatory deduction rule The parallel solutions rule 45

#10:RTQ & ATQ!! 2011 Question #1: The Combine 46

#10:RTQ & ATQ!! 2011 Question #1: The Combine 47

AP Statistics Exam Tips Recap #1: Get prepared! #2: Be a smart test taker. #3: Use technology wisely #4: Follow the 4-step inference process #5: Don’t shoot yourself in the foot! #6: Naked answer = no credit #7: If you can’t answer part of a question, don’t assume you can’t answer other parts #8: Know what distribution you’re talking about! #9: Don’t write too much! #10:RTQ & ATQ!! 48

Tips for Writing Free Response Questions on the AP Statistics Exam Laura Trojan Cannon School

Common Topics Exploratory Data Analysis –One-variable data Descriptive statistics: Center, Shape, Spread –Two-variable data Correlation, regression, residual plots, coefficient of determination Hypothesis Tests Probability Experimental Design 50

Common Task: Choose If asked to choose between two things (fuel additive A or fuel additive B), students should state why they would choose one AS WELL AS why they would NOT choose the other. –Think about “The Bachelor.” 51

Common Task: Compare If asked to compare, students should make less than/greater than statements. See sample question 1 from 2005 – K1 and S1. Compare like things. Never compare a median of one distribution to the 1st quartile of another. Instead, compare the median of distribution A to the median of distribution B. AP Questions often ask students to compare one-variable distributions. They’ll need to compare some measure of center, shape, and spread. 52

Common Task: Test of Significance Hypothesis Test rubrics generally look for four components: –State the hypotheses with the correct symbols. Define any subscripts. –Identify (by NAME or by FORMULA) a test-statistic. State and check the assumptions. –Calculate the value of the test-statistic. Calculate the p-value and compare it to alpha. Reject or fail to reject the null hypothesis. –State your conclusion in words in the context of the problem. 53

Writing Tips Be clear, brief, and explicit. Read the question. Answer the question. No more, no less. –Students who ramble on and on are likely to contradict themselves. Plus, when a student is succinct, it is clear that he/she knows what the question is asking and how to answer it. See sample question 1 from D1 and U2. 54

Writing Tips Tell students: never contradict yourself. If they asked to choose between items, TAKE A STAND. Make a choice. This isn’t the time to state what’s good and bad about both items. NEVER write calculator commands. –Never? Never. Never ever. Not even once. Period. 55

Writing Tips Be careful about strong language. –One sample design question asked why we randomly allocate subjects to treatment groups. If students stated that random allocation ELIMINATES bias, they were given NO credit. 56

Writing Tips Be careful about the converse of if/then statements. –If the distribution is skewed right, then the mean is greater than the median. –If the mean is greater than the median, then the distribution is skewed right. Can anyone give a counter-example? 57

Writing Tips Do not use pronouns! Paper “It is higher.” Reader “WHAT is higher?” Don’t use no double negatives. –I fail to reject that I don’t believe that the data are not independent. 58

Common Student Errors Failing to realize that when the directions say “Give appropriate statistical evidence to support your conclusion” or “Justify, using statistical evidence” students are being asked to conduct FORMAL hypothesis tests. Failing to realize that when students write the words “on average” that they’re referencing the mean. Using non-statistical words to convey a statistical concept. –The graph is “even.” ??? Does the student mean uniform? Symmetric? Normal? –The residual plot is “half above and half below.” I think the student meant randomly scattered. –The data are “consistent.” Does the student mean less variable? 59

Common Student Errors Making assumptions about how much they should write. The amount of space left for students to answer the question is NOT an indication of how much they should write. Not recognizing that expected value = mean. When stating assumptions, saying the data are normal. –The correct assumption is that the population is distributed normally. We check that assumption by looking at the distribution of the sample data. 60

Common Student Errors Confusing skewed right and skewed left. Confusing symmetric or bell-shaped with approximately normal. Confusing categorical data with quantitative data (or one-variable data with two-variable data) Listing everything they know and hoping that part of it is correct. –This often leads to a “parallel solution.” The graders will grade the weakest of the solutions. 61

Common Student Errors Confusing random sampling with random allocation. They need to know the difference between taking a simple random sample and randomly allocating subjects to treatment groups. Incorporating blocking schemes when blocking doesn’t make sense or might actually undermine the experiment. Editor’s note: you can’t spend too much time on experimental design!!! 62

Common Student Errors Confusing interpretations of the confidence LEVEL with interpretations of the confidence INTERVAL. Failing to state their results and interpret their results in the context of the problem. Name dropping. –Student answers, “Yes, because of the.” NO CREDIT!!! 63

In the end… It’s not what you know. It’s what you can PROVE that you know. 64

1.Don’t change an answer unless you have a reason of which you are very sure 2.State all assumptions & check conditions 3.Answer all parts of the Free Response questions – Make up an answer you don’t know if needed for the next part 4.Label and scale all graphs Mrs. Lerner’s Top AP Exam Tips 65

5.Don’t give ‘parallel’ solutions on the Free Response questions 6.Write neatly 7.Write all conclusions in context 8.Read all the words (just skimming “long scenario statements”) and understand what the question is asking (usually it is at the end) Mrs. Lerner’s Top AP Exam Tips 66

That’s it folks! OUR VERY BEST WISHES FOR YOUR SUCCESS IN THE AP EXAM(S) AND YOUR LIFE IF I CAN DO ANYTHING TO HELP, JUST LET ME KNOW Quick questions – call me at home cheers! 67