Critical Issues for Helping Students Perform Inference ...
Critical Issues for Helping Students Perform Inference Successfully and AP Stat Exam Tips! Mr. Lynch AP Statistics 1. Which Inference Method to Choose Estimating or testing a claim Confidence Intervals: 1. Identify Population of Interest and Parameter estimating
2. Identify correct procedure and VERIFY conditions for use 3. Carry out inference procedure 4. Interpret results in context Hypothesis Tests: 1. State Hypothesis in Words and Symbols (parameters) 2. Same 3. Calculate the test statistic (z or t) and P-value* (DRAW IT) 4. Draw a conclusion in context related to P-value or rejection region Means, proportions, relationships between categorical/ quantitative variables Need to know specific conditions required for the validity of each statistical inference procedure! (chart)
2. The different purposes of random selection and random assignment Random selection in sampling settings allows for generalizability Random assignment in experiments allows cause-and-effect conclusions Both permit the use of probability distributions as models in inference 3. How technology can be used as a tool for aiding inferential thinking Simulation to understand sampling
distributions (PAARC) Calculations for inference method No Calculator Syntax though! 4. Different inferential thinking in experiments and sampling Experiments: is there a treatment effect, or could the difference we observe be due to the chance involved in the random assignment? Sampling: could the difference we observe be due to chance variation in the sampling process?
5. Conditions for using each inference method, and why they are important Random sampling/Random assignment Normality Independence (of measurements/samples) 6. Distinguishing among samples, populations, and sampling distributions Connecting sampling distributions (what happens if we take many samples) and
inference (conclusions based on one sample) 7. Communicating effectively Using notation and statistical terminology correctly (demonstrates statistical intelligence) Stating technically correct conclusions in CONTEXT! Critical Issues for Helping Students Perform Inference Successfully
1. Which Inference Method to Choose 2. The different purposes of random selection and random assignment 3. How technology can be used as a tool for aiding inferential thinking 4. Different inferential thinking in experiments and sampling 5. Conditions for using each inference method, and why they are important 6. Distinguishing among samples, populations, and sampling distributions 7. Communicating effectively
AP Exam Scoring The AP Statistics Exam consists of two separate sections: Section I : 40 Multiple-Choice questions 90 minutes counts 50 percent of exam score SCORING: 1 point for each correct answer 0 points for each question left blank
Section II: Free-Response questions 90 minutes counts 50 percent of exam score Questions are designed to test your statistical reasoning and your communication skills. SCORING: Five open-ended problems @ 13 minutes; each counts 15 percent of free-response score One investigative task @ 25 minutes; counts 25 percent of free-response score Each free-response question is scored on a 0 to 4 scale. General descriptors for each of the scores are: 4: Complete Response: NO statistical errors and clear communication 3: Substantial Response: Minor statistical error/omission or fuzzy communication 2: Developing Response: Important statistical error/omission or lousy communication 1: Minimal Response: A "glimmer" of statistical knowledge related to the problem
0: Inadequate Response: No glimmer; statistically dangerous to himself and others Note: Your work is graded holistically, meaning that your entire response to a problem is considered before a score is assigned. Roxy Peck, Chief Reader 2001 Exam Answer Questions in Context! Many students state assumptions for inference, few actually check them! Sanderson Smith & Daren Starnes Biggest Challenge: what statistical technique to use on each question
RTFQ (Twice) Use appropriate statistical vocabulary Surveys,experiments,observational studies Familiarize yourself with formula sheet provided on AP Exam Know how to read a generic computer output Samples, sampling distributions, populations Insist that students verify conditions required for use of a statistical procedure before they carry it out! (CIs, Hyp Tests, Binom, Geom) During Exam
Relax, take time to think RTFQ carefully highlight, underline Look at graphs and displays carefully Graphing calculators: tool used sparingly, brain is primary tool! During Exam (MC) Ask: What statistical topic is being tested? Highlight key words/phrases
After deciding on an answer, look back to avoid careless mistakes or incorrect Assumps Always guess after eliminating bogus answers! If answer choice seems obvious careful obvious to others as well During Exam (FR)
Read all 5 FR questions 1st! Q1-meant to be straightforward Do the FRQs you feel confident about Do #6: Investigative task! What statistical concept is being tested? Dont have to answer a FRQ in paragraph form, bullets or algebraic process may be preferable Answer each Q in context! Specific Advice on FRQs
Graphs: Label and scale axes! Dont refer to a graph on your calculator, transfer it to your exam paper, burden of good communication. Communicate your thinking clearly Organize thoughts, write neatly Write efficiently: Get in, get out! Communicate: dont leave it to reader to make inferences
Avoid personal insights in your responses Graphing Calculator Use Dont waste time punching numbers (statistical intelligence?) Avoid Calculator syntax (normalcdf, 1-PropZTest, etc) Specific Advice on FRQs ATFQ Explain or Justify Do it! Dont write down everything you know! Dont give multiple/parallel solutions Notes:
Amount of space provided does not necessarily indicate how much to write If you can not get an answer to part of a question, make up a plausible answer to use in the remaining parts of the problem!
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