AP Statistics Exam Tips

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

2. Key Links • Today’s Resources • http://tinyurl.com/APS-2017-UNCC • Inference • http://tinyurl.com/inf-practice • http://tinyurl.com/Inf-wrong • Great MC Practice (pg 20-26) • AP Stats course description

3. KNOW YOUR EXAM!12 Years - Questions & Answers https://apstudent.collegeboard.org/apcourse/ap-statistics/exam-practice Or go to http://www.collegeboard.com • AP (2nd Item, top menu bar) • Get Practice Questions (1st row, right blue box) • Scroll down to AP Statistics

4. 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?

5. 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!

6. Multiple Choice [90 minutes – 40 questions] • Answer every question . (period) • Answer every question . (period) • Do all work in test book and circle answers there – but no work/answers in the test book is graded • Only bubble when you are done [Dr. D. view] – but leave time to bubble. • Please DO YOUR BEST to NOT ERASE!.

7. 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 • BubbleBEST ANSWER in the context of the question • Possible: No answer choice may be precisely correct or • Possible: More than one choice may be correct

8. 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 HighlightingBUT YOU CAN WRITE ON THE TEST • Weakly erased answers or stray marks often result in wrong scanned scores – and no one will know that!

9. 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) • Think about the intent of the question (what content is the author trying to find out if you know) • Reread the stem -- thinking about the precise question and intent • Determine the most likely answer(s)

10. Multiple Choice ExamplePage 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

11. Multiple Choice ExamplePage 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?

12. Multiple Choice ExamplePage 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?

13. Multiple Choice ExamplePage 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

14. 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) • Think about the intent of the question (what content is the author trying to find out if you know) • Reread the stem -- thinking about the precise question and intent • Determine the most likely answer(s)

15. 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 --- Suggest BUBBLE ANSWERS AT THIS END remember it • If Not sure, leave possible choices unmarked (you should designate the answer that seems most likely). Mark this question (On the test only) and return to it later

16. Multiple Choice Questions • Often as you do a test you will get an idea FOR 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 most kids finish the MC test in one hour so you should have plenty of time to go back. • Do not bubble early to minimize erasers • BUBBLE in the last 10 minutes (WATCH YOUR TIME) .

17. Multiple Choice Questions #4 • Often as you do 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 most kids finish the MC test in one hour so you should have plenty of time to go back. • Do not bubble early to minimize erasers • BUBBLE in the last 10 minutes (WATCH YOUR TIME) . • 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 PERFECT answer

18. The Free Response Section

19. 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!

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

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

22. 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!

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

24. Free Response Scoring • 1st 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

25. Free Response Ideas • Readers “are on your side” and award 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)

26. 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 – often only some of the space is needed!

27. Misc – But Important • You can bring two calculators to the exam • 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”

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

29. 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

30. 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.”

31. 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.

32. 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.

33. 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 2005 - D1 and U2.

34. 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.

35. 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.

36. 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?

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

38. 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?

39. 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.

40. 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.

41. 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!!!

42. 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 <insert theorem name here>.” NO CREDIT!!!

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

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

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

46. 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 • Lewis.Davidson@cms.k12.nc.us • Cheers!