Tips for Writing Free Response Questions on the AP Statistics Exam

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Tips for Writing Free Response Questions on the AP Statistics Exam

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Tips for Writing Free Response Questions on the AP Statistics Exam

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Tips for Writing Free Response Questions on the AP Statistics Exam

Laura Trojan

Cannon School

- Exploratory Data Analysis
- One-variable data
- Descriptive statistics: Center, Shape, Spread

- Two-variable data
- Correlation, regression, residual plots, coefficient of determination

- One-variable data
- Hypothesis Tests
- Probability
- Experimental Design

- 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.”

- If asked to compare, students should make less than/greater than statements.
- See sample question 1 from 2005 – K1 and S1.

- 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.

- 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.

- 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.

- 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.

- 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.

- 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?

- Do not use pronouns!
- “It is higher.” WHAT is higher?

- I fail to reject that I don’t believe that the data are not independent.

- 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?

- 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.

- 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.

- 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!!!

- 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!!!

- It’s not what you know.
- It’s what you can PROVE that you know.