Download Simple Things Students Can Do To Improve Their AP Exam Scores

Simple Things Students Can Do To Improve Their
AP Exam Scores
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1. Read the problem carefully, and make sure that you understand the question that is asked.
Then answer the question(s)!
Suggestion: Circle or highlight key words and phrases. That will help you focus on exactly what
the question is asking.
Suggestion: When you finish writing your answer, re-read the question to make sure you haven’t
forgotten something important.
2. Write your answers completely but concisely. Don’t feel like you need to fill up the white space
provided for your answer. Nail it and move on.
Suggestion: Long, rambling paragraphs suggest that the test-taker is using a shotgun approach
to cover up a gap in knowledge.
3. Don’t provide parallel solutions. If multiple solutions are provided, the worst or most egregious
solution will be the one that is graded.
Suggestion: If you see two paths, pick the one that you think is most likely to be correct, and
discard the other.
4. A computation or calculator routine will rarely provide a complete response. Even if your
calculations are correct, weak communication can cost you points. Be able to write simple
sentences that convey understanding.
Suggestion: Practice writing narratives for homework problems, and have them critiqued by your
teacher or a fellow student.
5. Beware careless use of language.
Suggestion: Distinguish between sample and population; data and model; lurking variable and
confounding variable; r and r2; etc. Know what technical terms mean, and use these terms
correctly.
Simple Things Students Can Do To Improve Their
AP Exam Scores
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6. Understand strengths and weaknesses of different experimental designs.
Suggestion: Study examples of completely randomized design, paired design,
matched pairs design, and block designs.
7. Remember that a simulation can always be used to answer a probability question.
Suggestion: Practice setting up and running simulations on your TI-83/84/89.
8. Recognize an inference setting.
Suggestion: Understand that problem language such as, “Is there evidence to show
that … ” means that you are expected to perform statistical inference. On the other
hand, in the absence of such language, inference may not be appropriate.
9. Know the steps for performing inference.
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hypotheses
assumptions or conditions
identify test (confidence interval) and calculate correctly
conclusions in context
Suggestion: Learn the different forms for hypotheses, memorize
conditions/assumptions for various inference procedures, and practice solving
inference problems.
10. Be able to interpret generic computer output.
Suggestion: Practice reconstructing the least-squares regression line equation from
a regression analysis printout. Identify and interpret the other numbers.
The Hardest (<50% correct) Multiple Choice Questions
from the 2002 AP Statistics Exam
• 9. (39% correct) A volunteer for a mayoral candidate’s campaign
periodically conducts polls to estimate the proportion of people in the city
who are planning to vote for this candidate in the up coming election.
Two weeks before the election, the volunteer plans to double the sample
size in the polls. The main purpose of this is to
(A) reduce nonresponse bias
(B) reduce the effects of confounding variables
(C) reduce bias due to the interviewer effect
(D) decrease the variability in the population
(E) decrease the standard deviation of the sampling distribution of the
sample proportion
• 9. Answer: (E) The standard deviation of the sampling distribution is . If
the sample size is increased, then the value of this fraction will decrease.
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(A)
(B)
(C)
(D)
(E)
10. (37% correct) The lengths of individual shellfish in a population of
10,000 shellfish are approximately normally distributed with mean 10
centimeters and standard deviation 0.2 centimeter. Which of the following
is the shortest interval that contains approximately 4,000 shellfish lengths?
0 cm to 9.949 cm
9.744 cm to 10 cm
9.744 cm to 10.256 cm
9.895 cm to 10.105 cm
9.9280 cm to 10.080 cm
10. Answer: (D) The "shortest interval" tells me to use a symmetric interval
about the mean, µ = 10. If 4,000 out of 10,000 will be IN the interval, then
6,000 out of 10,000 will be OUTSIDE the interval. So there is 0.3 area
under the curve and ABOVE the interval I'm looking for, and 0.3 area
BELOW the interval. TI-83: invNorm(.7,10,.2) = 10.105, and
invNorm(.3,10,.2) = 9.895. Hence the shortest interval containing 4,000
shellfish is (9.895, 10.105).
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I.
II.
III.
(A)
(B)
(C)
(D)
(E)
18. (29% correct) Which of the following statements is (are) true
about the t-distribution with k degrees of freedom?
The t-distribution is symmetric.
The t-distribution with k degrees of freedom has a smaller variance
than the t-distribution with k + 1 degrees of freedom.
The t-distribution has a larger variance than the standard normal (z)
distribution.
I only
II only
III only
I and II
I and III
18.Answer: (E) The t-distribution is shorter at the center (mean) and has
more area in the tails. Statement II is wrong because as the sample
size increases, the t–distribution approaches the normal distribution,
and has less area in the tails, and hence a smaller variance.
Ten Lessons Learned
from the AP Reading
#10: Read the question--twice!
2008 AP Exam, Free Response Question 1
To determine the amount of sugar in a typical serving of
breakfast cereal, a student randomly selected 60 boxes of
different types of cereal from the shelves of a large grocery
store. The student noticed that the side panels of some of the
cereal boxes showed sugar content based on one-cup
servings, while others showed sugar content based on threequarter-cup servings. Many of the cereal boxes with side
panels that showed three-quarter-cup servings were ones
that appealed to young children, and the student wondered
whether there might be some difference in the sugar content
of the cereals that showed different-size servings on their side
panels.
#10: Read the question--twice!
To investigate the question, the
data were separated into two
groups. One group consisted of
29 cereals that showed one-cup
serving sizes; the other group
consisted of 31 cereals that
showed three-quarter-cup
serving sizes.
The boxplots display sugar
content (in grams) per serving of
the cereals for each of the two
serving sizes.
#10: Read the question--twice!
2008 AP Exam, Free Response Question 1
To determine the amount of sugar in a typical serving of
breakfast cereal, a student randomly selected 60 boxes of
different types of cereal from the shelves of a large grocery
store. The student noticed that the side panels of some of the
cereal boxes showed sugar content based on one-cup
servings, while others showed sugar content based on threequarter-cup servings. Many of the cereal boxes with side
panels that showed three-quarter-cup servings were ones
that appealed to young children, and the student wondered
whether there might be some difference in the sugar content
of the cereals that showed different-size servings on their side
panels.
#10: Read the question--twice!
To investigate the question, the
data were separated into two
groups. One group consisted of
29 cereals that showed one-cup
serving sizes; the other group
consisted of 31 cereals that
showed three-quarter-cup
serving sizes.
The boxplots display sugar
content (in grams) per serving of
the cereals for each of the two
serving sizes.
#9: Answer the question!
(a) Write a few sentences to compare the distributions of sugar
content per serving for the two serving sizes of cereals.
Shape
1-cup: Left skewed
¾-cup: Roughly symmetric
Center More sugar for 1-cup
cereals than ¾-cup cereals
(medians are 13g & 10g)
Spread More variability for 1-cup
cereals than ¾-cup cereals
(IQRs are 11g & 4 g)
#8: Don’t shoot yourself in the foot!
• Shape
– Skewed which way?
– “Normal”?!
• Center
– Mean?!
• Spread
– Standard deviation?!
#7: Avoid calculator speak
(1) Binompdf(12,.2,3) = no full credit
• Better: P(X = 3) = (12C3)(0.2)3(0.8)9
• OK: binompdf with n = 12, p = .2, k = 3
(2) Normalcdf(90,105,100,5) = no full credit
• Better: draw, label, shade Normal curve
• OK: normalcdf with low bound = 90, high
bound = 1-5, mean = 100, std. dev. = 5
#6: Naked answer = no credit
• Directions: Show all your work. Indicate clearly the
methods you use, because you will be graded on the
correctness of your methods as well as on the
accuracy and completeness of your results and
explanations.
From 2008 Exam, FR Question 3
• “Calculate the expected score for each player.”
• “Find the probability that the difference in their
scores is -1.”
#5: Know your inference methods
2008 AP Exam, Free Response Question 5
A study was conducted to determine where moose are
found in a region containing a large burned area. A
map of the study area was partitioned into the
following four habitat types.
(1) Inside the burned area, not near the edge of the
burned area,
(2) Inside the burned area, near the edge,
(3) Outside the burned area, near the edge, and
(4) Outside the burned area, not near the edge.
The study area
The figure below shows these four habitat types.
The proportion of total acreage in each of the habitat types
was determined for the study area.
Aerial survey results
Using an aerial survey, moose locations were
observed and classified into one of the four
habitat types. The results are given in the
table below.
#5: Know your inference methods
(a) The researchers who are conducting the
study expect the number of moose observed
in a habitat type to be proportional to the
amount of acreage of that type of habitat. Are
the data consistent with this expectation?
Conduct an appropriate statistical test to
support your conclusion. Assume the
conditions for inference are met.
#5: Know your inference methods
• What percent of students at your school have
a MySpace page?
• Is there a relationship between students’
favorite academic subject and preferred type
of music at a large high school?
• Helpful web site: INSERT URL
#4: Don’t skip the investigative task
Part B
Question 6
Spend about 25 minutes on this part of the
exam.
Percent of Section II score—25
#3: Beware mandatory deductions
• Saying “experiment” for an observational
study
• “Confounding” when there isn’t
• Using incorrect symbols: eg statistics in a
hypothesis
#2: Only use terms and symbols you know
• It’s better to explain in your own words than
to use a technical term incorrectly
• If you’re unsure about notation, use words
instead of symbols
#1: Don’t write too much
• Answer the question, then shut up!
• Space provided is more than enough
• Remember the mandatory deduction rule
Ten Lessons Learned: Recap
#10: Read the question--twice!
#9: Answer the question!
#8: Don’t shoot yourself in the foot!
#7: Avoid calculator speak
#6: Naked answer = no credit
#5: Know your inference methods
#4: Don’t skip the investigative task
#3: Beware mandatory deductions
#2: Only use terms and symbols you know
#1: Don’t write too much