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

Successfully1. Which Inference Method to Choose2. The different purposes of random selection and

random assignment3. How technology can be used as a tool for aiding

inferential thinking4. Different inferential thinking in experiments and

sampling5. Conditions for using each inference method, and why

they are important6. Distinguishing among samples, populations, and

sampling distributions7. 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

scoreSCORING:1 point for each correct answer0 points for each question left blank

• Section II: Free-Response questions 90 minutes counts 50 percent of exam scoreQuestions 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 scoreOne 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 communication3: Substantial Response: Minor statistical error/omission or fuzzy communication2: Developing Response: Important statistical error/omission or lousy communication1: Minimal Response: A "glimmer" of statistical knowledge related to the problem0: 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! (CI’s, 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 FRQ’s you feel confident about• Do #6: Investigative task!• What statistical concept is being tested?• Don’t have to answer a FRQ in paragraph

form, bullets or algebraic process may be preferable

• Answer each Q in context!

Specific Advice on FRQ’s

• Graphs: Label and scale axes!– Don’t 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: don’t leave it to reader to make inferences– Avoid personal insights in your responses

• Graphing Calculator Use– Don’t waste time punching numbers (statistical intelligence?)– Avoid Calculator syntax (normalcdf, 1-PropZTest, etc)

Specific Advice on FRQ’s

• ATFQ– “Explain” or “Justify” Do it!– Don’t write down everything you know!– Don’t 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!