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F 5/1/09
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Make-Up
Test, 7:00 a.m., Room LJ-302 (Mathplex North). If you missed the tests on both Wednesday and
Thursday, then you may make up only one of them, and the other one will be your
dropped test for the quarter. If you missed only one of the tests, you may
elect to treat it as your dropped test, in which case you do not need to take
a make-up.
HW due in class: Free-response questions (two “shorts” and a “long”) from
yesterday. As discussed in class, I would like this today, but I would rather
receive it next week than not at all.
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T 5/5/09
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AP Exam,
1:00 p.m., Trophy Room.
What to bring: several sharpened
pencils, TI-83 or TI-84 graphing calculator, spare batteries.
What to leave at home or in your car: cell
phone, scratch paper, non-graphing calculator, PDA, etc. The College
Board is apparently afraid of the possibility that students will communicate
illegally during the exam or hide contraband electronic devices disguised as
generic calculators.
Format of the exam is as follows:
Part I (90 minutes): 40 multiple-choice questions, calculator allowed.
Bathroom break.
Part II (90 minutes): 6 free-response questions, calculator allowed.
In Part I, questions are scored as 4 points if correct, 0 points if omitted,
and –1 point if answered incorrectly. There is no partial credit.
In Part II, there are 5 “short” problems for which you should allocate
approximately 13 minutes each, plus one “long” project-style problem for
which you should allocate approximately 25 minutes. The practice exams in
your Barron’s review book show this format precisely. Each problem is graded
holistically on a scale from 0 (clueless) to 4 (essentially correct).
Standard mathematical notation is required, and you must work top to bottom,
left to right. It is best to place one equation, thought, or idea per line.
Circle or box your answers. You must justify your answers adequately, since
answers with no support will result in (at best) only partial credit. Instead
of erasing large sections, you should simply make an “X” through anything you
wish to be ignored. In statistical tests, you should follow the PHASTPC
format, including naming the test and checking assumptions properly (see
example below). All decimal answers should have at least 3 or 4 significant
digits of accuracy, and that means that you should never round your intermediate results. For example, if the answer
to a probability question is 153 out of 10 million, do not round your answer
to 0.00002.
Your exam score is computed by an equal weighting of the multiple-choice and
free-response portions. Score cutoffs vary from year to year but are normally
in the 70% range for a 5 (high pass).
Here are some examples of what you
might write for the “A” step in a PHASTPC test (identify the test, then state and check all assumptions):
Assumptions for 2-prop. z test:
- Two independent SRS’s?
Yes (given) ü
- Both pops. large?
N1 = 5000 = 50(100)
= 50n1  10n1 ü
N2 is essentially
infinite ü
 all at least
5?
Yes, observed counts were given as 15, 35, 21, and 19, resp. ü
Assumptions for 2-sample t test:
- Two independent SRS’s?
Yes (given) ü
- Both pops. normal?
No, but since n1 =
8 and n2 = 12, we
have n1 + n1 = 20 15.
Since no outliers and only mild skewness (given), samples are large
enough. ü
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Th 5/7/09
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HW due: First draft of group project proposal. Don’t
worry: Anything that is too much work, unethical, or otherwise unsuitable
will be rejected, and you will be able to write a better draft for tomorrow.
If the group leader is unable to attend class for any reason, he must
deputize somebody else to deliver it so that we can discuss all the
proposals.
Here are some ideas to consider in case you cannot think of anything:
1. Is video game performance impaired by context switching? (To test this
notion, you would need a video game in which score is a function of time, but
in which time is paused whenever the window focus is on another application,
such as e-mail, iTunes, or IM.)
2. How random is the pseudorandom algorithm of the TI-83/84 (or Smokey, if
you prefer)? Do a number of screening tests (e.g., testing for odd/even
pairs, ascending triples, or anything else you can dream up) and a follow-up
test for any outputs that look suspiciously nonrandom. Remember, some of
those will probably be nothing more than Type I error.
3. How accurate are various groups of people in gauging the age (or IQ, or
ethnicity, or whatever) of speakers when the only information provided is a
digital audio sample?
4. How accurate are people at identifying “straight vs. gay”? John Stossel of
ABC’s 20/20 did a story on this
several years ago. You could probably do a higher-quality study yourself.
5. What is the relationship, if any, between height and longevity? The answer
is surprisingly complicated, and there is no general agreement.
6. The spinning
dancer optical illusion is mysterious. Some people see the dancer
spinning clockwise, while others see her spinning counterclockwise. A few
people can make her seem to spin either way at will. What association, if
any, exists between these different views of the illusion and other
characteristics of the subject (handedness, age, height, number of siblings,
gender, etc.)? Are subjects more likely to see the illusion in a certain way
depending on how they are primed? depending on what frame of the animation is
the first one displayed? There are many interesting questions that could be
researched.
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