Transcript Tips for Writing Free Response Questions on the AP Statistics Exam

Tips for Writing Free Response
Questions on the AP Statistics
Exam
Laura Trojan
Cannon School
Common Topics

Exploratory Data Analysis
 One-variable
 Descriptive
data
statistics: Center, Shape, Spread
 Two-variable
data
 Correlation,
regression, residual plots, coefficient
of determination
Hypothesis Tests
 Probability
 Experimental Design
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Common Task: Choose
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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.
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Think about “The Bachelor.”
Common Task: Compare
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If asked to compare, students should make
less than/greater than statements.
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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.
Common Task: Test of Significance
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Hypothesis Test rubrics generally look for four
components:
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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.
Writing Tips

Be clear, brief, and explicit. Read the
question. Answer the question. No
more, no less.
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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.
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See sample question 1 from 2005 - D1 and U2.
Writing Tips
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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.
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.
Writing Tips
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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.
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Can anyone give a counter-example?
Writing Tips
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Do not use pronouns!
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“It is higher.” WHAT is higher?
Don’t use no double negatives.
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I fail to reject that I don’t believe that the
data are not independent.
Common Student Errors
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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.
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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?
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.
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The correct assumption is that the population is
distributed normally. We check that assumption by
looking at the distribution of the sample data.
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.
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This often leads to a “parallel solution.” The graders
will grade the weakest of the solutions.
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.
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Editor’s note: you can’t spend too much time on
experimental design!!!
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.
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 Student
answers, “Yes, because of the <insert
theorem name here>.” NO CREDIT!!!
In the end…
It’s not what you know.
 It’s what you can PROVE that you know.
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