Transcript here - VealeyMath

Get Ready for the AP Exam
Before the AP Exam
• Be able to describe a distribution of data
(center, shape and spread)
• Be able to calculate 5-number summary,
IQR and outliers
• Be able to draw boxplot, histogram,
etc…know when to use which one.
• Know how to read generic computer
output.
Before the AP Exam
• Know the difference between a scatter plot and
a residual plot.
• Know that a model that produces predicted
values isn't providing actual data values. If the
equation for a least-square regression line is y =
1.5x + 3.34, then the slope and y-intercept need
to be interpreted properly. For instance, one
might say that "on the average, a unit change in
x results in a change of 1.5 units in y" and that
"the predicted value of y is 3.34 when x = 0."
Before the AP Exam
• Know correlation coefficient and coefficient of
determination & be able to interpret in context.
• Don't confuse coefficient of correlation and slope
of least-squares regression line.
– A slope close to 1 or -1 doesn't mean strong
correlation.
– An r value close to 1 or -1 doesn't mean slope of
least-squares regression line is close to 1 or -1.
– Relation between b (slope of regression line) and r
(coefficient of correlation) is b = r(Sy/Sx). This is on
formula sheet provided for the exam.
– Remember that r2 > 0 doesn't mean r > 0. For
instance, if r2 = 0.81, then r = 0.9 or r = -0.9.
Before the AP Exam
• Remember that the least-squares regression line
contains the point (mean x, mean y), where mean x is
the mean of the x-values, and mean y is the mean of the
y-values.
• A coefficient of correlation near 0 doesn't necessarily
mean there are no meaningful relationships to be
observed between the two data sets. Whenever
possible, look at the "shape" of the data.
• Realize that logarithmic transformations can be practical
and useful. Among other things, taking logs cuts down
the magnitude of numbers. Also, if {(x,y)} has an
exponential pattern, then {(x,log y)} has a linear pattern.
Before the AP Exam
• Know the formulas and be able to write them out!
• Know Simpson’s Paradox: The effects of lurking
variables can change or even reverse relationships
between 2 categorical variables. This can result
when data from several groups are combined to form
a single group.
• Binomial vs Geometric
• Discrete Random Variable
• Central Limit Theorem
• Law of Large Numbers
Before the AP Exam
• Know the different inference tests and be able
to conduct a significance test and confidence
interval in the appropriate situation.
• Only pool for 2-sample z proportions
• Know that the null and alternate hypotheses
are stated in terms of population parameters, not
sample statistics.
• Know the different assumptions and formulas for
the different inference tests
• Know Type I, Type II, and Power ** Type II and
Power are z-score concepts
Before the AP Exam
• Adjust width of confidence interval
• Standard deviation vs Variance
Before the AP Exam
• Know the difference between an observation and an
experiment
• Understand the difference between a simple random
sample and the random assignment of treatment to
subjects.
• Understand that there are two types of replication in
experiments: (1) Replication within the experiment
quantifies variablility within the experiment, and (2)
replication of the experiment helps achieve validation.
• Understand terms like confounding, lurking variables,
etc.
• Know different types of sampling.
• Know different types of experimental design
Before the AP Exam
• Be careful with the concept of simple random sample
(SRS).
• If each individual in a group has an equal probability of
being chosen in a sample, it doesn't follow that the
sample is an SRS.
• Example: Consider a class of 6 boys and 6 girls. I want
to randomly pick a committee of two students from this
group. I decide to flip a coin. If "heads," I will choose two
girls by a random process. If "tails," I will choose two
boys by a random process. Now, each student has an
equal probability (1/6) of being chosen for the committee.
However, the chosen two students do not represent an
SRS of size two picked from members of the class, for
the selection process does not allow for a committee
consisting of one boy and one girl. To have an SRS of
size two from this class of 6 boys and 6 girls, each
committee of two students would have to have an equal
probability of being chosen.
Multiple Choice Questions
• You don't have to answer all of the questions to get a
good overall score.
• If an answer is "obvious," think about it. If it's so obvious
to you, it's probably obvious to others... and the chances
are good that it is not the correct response. For example,
suppose one set of test scores has a mean of 80, and
another set of scores on the same test has a mean of
90. If the two sets are combined, what is the mean of the
combined scores. The "obvious" answer is 85 (and will
certainly appear among the answer choices), but you, as
an intelligent statistics student, realize that 85 is not
necessarily the correct response.
Multiple Choice Questions
If a question and/or answer choice set
appears to be detailed and you need to do
a lot of reading to reach a conclusion,
most of the answer choices will probably
be obviously incorrect. Don't be frightened
off by questions and/or answer set choices
that seem to be wordy. Just read carefully,
and use the highlighting technique
previously mentioned.
AP Free Response Questions
• Read a problem carefully, sentence by
sentence.
• Relate to the problem. Decide what statistical
concept/idea is involved. This will allow you to
make an intelligent approach to questions
asked. If you get started on an intelligent path,
you will probably get some points even if you
make some mistakes along the way.
AP Free Response Questions
• Be neat, Make it clear to the reader what you are
attempting to do. However, don't write too much. Overkill
can waste valuable time. And if you contradict yourself,
will count against you.
• Questions may well look very detailed. You may be
given much more information than you actually need.
This is likely to be true if you are shown a computer
printout. Don't get flustered by the way a problem "looks"
when you first glance at it. * Some questions may give
you considerable leeway in choosing an approach to a
solution. Consider your options carefully and take the
one that requires the least amount of time.
AP Free Response Questions
• Don't be calculator-inefficient. It is certainly
possible to waste time punching numbers
into a calculator. Entering lists of numbers
into a calculator can be time-consuming,
and certainly doesn't represent a display of
statistical intelligence. If, upon reading an
AP question, you think you will have to
enter many numbers into a calculator, you
are probably overlooking something.
Reread the problem, and look for a quicker
path to a solution.
Just Before Exam Day
• The night before get plenty of sleep!
• You are done studying 2 nights before
your AP Exam. Look over your notes the
night before (briefly)!
• Make sure you pack your calculator with
working batteries, extra batteries and
pencils/erasers the night before. Bring a
backup calculator if necessary.
AP Exam – The Big Day
• Relax, and think. Remember that everyone else
taking the exam is in a situation identical to
yours. Realize that the problems will probably
look detailed compared to problems you have
encountered in other math courses.
• Pace Yourself.
– Multiple Choice – skip problems, mark them and
come back. Guess an answer if narrow down to 3
choices.
– Free Response – do problem 1 then problem 6 then
the rest in order of difficulty.
During the AP Exam
• Use the language of statistics in the context of
the problem. Give answers that make sense in
the context of the problem. For instance, it
generally makes no sense to talk about "1/3 of
an airplane."
• Don’t be sloppy in choice of words. For instance,
on a residual graph, the phrase "half are above
and half are below" is not equivalent to
"randomly scattered.“
• Define symbols you introduce.
During the AP Exam
• Be careful when using "calculator language." It is
important for a reader to understand what is
written and feel that you really know and
understand what you wrote as a response to a
problem.
• Look at graphs and displays carefully. For
graphs, note carefully what is represented on
the axes, and be aware of number scale. Some
questions that provide tables of numbers and
graphs relating to the numbers can be answered
simply by "reading" the graphs.
During the AP Exam
When AP instructions say "Give appropriate statistical evidence to
support your conclusion," or "Justify, using statistical evidence," this
means you need to conduct a formal hypothesis testing. This
includes:
1. Stating the hypothesis in context of the problem.
2. Naming the test used and why it was used, and checking (not just
naming) the conditions or assumptions for the test used. A rough
sketch of the "shape" of the data might be helpful here.
3. Carrying out the mechanics of the test and giving a numerical test
statistic and a p-value.
4. Writing the conclusion in context. The test statistics must be
linked to the conclusion. Example: "Since the p-value is so small
(alpha < .05), I reject the null hypothesis and conclude that there is
no association between hikers ability and direction traveled when
lost."
During the AP Exam
• Don’t mix up the null and alternate hypothesis.
• Always check assumptions for significance tests
AND confidence interval
• When given data, always check assumptions
instead of just saying something like "it is
assumed....". For instance, in a chi-square test
where cell counts are known, if all expected
counts are greater than or equal to 5, this should
be noted, as contrasted to just stating the
assumptions for chi-square.
• Interpret p-values correctly and in the context of
the problem.
After the AP Exam
• When it is over, you are done.
• If you know you prepared to the best of your
ability and you tried to do the best job you could
on the test, then that is the best anyone can ask
of you (even me).
• So stop worrying about your score…..(yeah, I
know that’s easy for me to say, I didn’t take the
test)!
• You will know your score before I do – email me!