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T 11/1/05
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HW due:
Write a research question and a proposal for an experiment you would really
like to conduct. Indicate specifically how you will address the problems of control, randomization, and replication
in your design. Hint: After you
write the general description of your methodology, it is best if you actually
have a section with 3 bullet points labeled “control,” “randomization,” and
“replication,” and a few lines of description to accompany each.
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W 11/2/05
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HW due:
Write a slightly better research question and proposal, except that this time
there is one submission required per
group. Jeffrey P. is the group leader of group 5, with Henry P. and
Michael L. Kenny K. is the group leader of group 1, with Greg C. and Chris R.
Please use the telephone to communicate with your group members.
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Th 11/3/05
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HW due:
Using the feedback provided in class, rewrite your group proposal slightly and
correct the typos and grammatical errors, if any. Also, add more detail to
your methodology so that it is clear exactly how you will conduct the
experiment. The approximate length will be one page, typewritten,
single-spaced. One submission is required from each group. Group leaders
should deputize someone if they are unable to attend class or fulfill their
group leader duties.
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F 11/4/05
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No school.
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M 11/7/05
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HW due:
Read Richard Morin’s “Unconventional Wisdom” column in the Sunday Washington Post Outlook section, as
well as this online
chat that he conducted on Oct. 24 concerning his in-depth survey of local
and national teens.
In class: Quiz on “Unconventional
Wisdom” (4 pts.).
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T 11/8/05
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Quiz (10
pts.) on symbolic logic. This is a review from Form III geometry. If you took
good notes yesterday, you should be able to perform the manipulations needed.
Remember, P Þ Q is
equivalent to saying that P is
false or Q is true, i.e., ~P Ú Q.
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W 11/9/05
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HW due:
Answer the following probability questions:
1. You toss a fair die 10 times. Compute (a) the probability of obtaining no
odd-numbered rolls, and (b) the probability of obtaining at least 1
odd-numbered roll.
2. In 7 rolls of a fair die, compute the probability that the numbers 2 or 3
are seen at least once.
3. There are 104 commercial nuclear reactors in the U.S. If the probability
of a core meltdown at any one plant in any one year is .0001 (a figure
sometimes used by the nuclear industry itself), and if this probability is
independent across years and across plants (an unrealistic assumption, to be
sure, but we will make it in this problem), then compute the probability of
at least one core meltdown in the U.S. in the next 30 years.
In class: Graded Discussion on the
online
chat contents. You do not need to memorize the statistics in the online
chat, but you need to be sufficiently familiar with all the topics discussed
so that you can participate intelligently. For example, at one point, the
number 65% was given as the percentage of Washington-area high school
students who had taken an AP or IB course. It would be sufficient for you to
know that about two thirds of Washington-area high school students, according
to the poll, have enrolled in an advanced class of this type.
As illustrated in yesterday’s dry run, questions will be tossed to randomly
selected students, who will need to answer them to the best of their ability.
The person who receives the question, even if he fumbles it, becomes the
moderator for that round and must choose other people to discuss matters
related to that question’s topic. If the discussion lags, the student
moderator for that round will need to ask additional related questions.
Talking out of turn is prohibited. I will sit in the corner and take notes, scoring
each student based on knowledge of the material, ability to apply course
knowledge, quality of discussion, and politeness.
You may use one small note card (3 inches by 5 inches), but no printouts.
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Th 11/10/05
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HW due: If
you scored a 4 on yesterday’s HW assignment, please make sure that your
answers are as shown below, and you may make corrections on your original
sheet. If you scored less than a 4, you need to re-do the entire assignment on a fresh sheet of paper. Show all
work.
Answers (WARNING: You will earn no
credit unless you also show supporting work.)
1.(a) P(no odd rolls) = 1/1024
(b) P(at least
one odd roll) = 1023/1024
2. P(at least one 2 or 3) =
2059/2187 » .941
3. P(at least one core meltdown) » .268
Then, complete as much of the STA Mathcross
#1 as possible. You may seek help from your classmates, from your
parents, and from the Internet, but not from students of mine in other
classes. There will be a prize for the best entry.
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F 11/11/05
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HW due:
Read pp. 161-167 and answer the following questions.
1. Do “mutually exclusive” and “independent” mean the same thing? If so,
provide a sample word problem with numbers and solutions. If not, explain the
difference in your own words.
2. If 3 cards are drawn without replacement from a well-shuffled deck,
compute the probability that all 3 cards are from the same suit. Show your
work.
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M 11/14/05
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HW due: Read
pp. 167-172; write p. 181 #2, 3, 4. Write a short paragraph of explanation
for each one, in your own words. Also finish the STA Mathcross #1 if possible.
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T 11/15/05
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HW due:
Read pp. 173-175 thoroughly and explain the bracketed solution at the end of
Example 9.28. Be sure to perform the calculator operations described in the
reading as you proceed.
Quiz: There may be a short quiz on
the purpose of binompdf, binomcdf, geometpdf, and geometcdf. You may use your
calculator manual during the quiz if you still have it.
Also: David C.’s unclaimed T-shirt will be awarded to the STA Mathcross #1 high scorer.
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W 11/16/05
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HW due:
Answer the following questions.
1. The probability that a box of chocolates is underweight (i.e., less than
the stated net weight) is p = 0.01.
Clearly, this is a fairly rare occurrence. Assume that the probability is
independent of lot and does not change from day to day. Occurrences of
underweight boxes are uniformly random and are scattered throughout each
day’s production. Let X = the
number of underweight boxes in a randomly chosen lot of 150 boxes.
(a) Is X a binomial random
variable? Why or why not?
(b) Compute the expected number of underweight boxes in each day’s production
of 15,000 boxes.
(c) Compute the expected number of underweight boxes in each lot of 150
boxes.
(d) Compute the probability distribution of X. In other words, list the first few possibilities for X, namely 0, 1, 2, 3, 4, . . ., and
compute the probability for each.
(e) Compute the probability that X
is less than 2. Use this notation: P(X < 2).
(f) Compute P(X > 0).
(g) Compute the probability that X
is between 1 and 3, inclusive. Use correct notation.
(h) Compute the probability that X
is greater than 2.
2. Mr. Hansen is a terrible free-throw shooter. In fact, despite practicing
diligently to be on his 6th-grade basketball team, a team that was so
horrible that it lost every game in the season, he was never able to rise
above the rank of team statistician. Let p
= .2 be the probability of Mr. Hansen’s sinking a free throw, and assume that
the shooting events are independent. Let Y
= the number of shots needed in order to sink the first free throw.
(a) Compute q.
(b) What does q mean? (Use correct
notation.)
(c) Explain why P(Y = 3) = q2p.
(d) Explain why P(Y = n) = qn
– 1p for any positive integer
n.
(e) Compute P(Y £ 3).
(f) Compute P(Y > 5).
(g) Compute P(Y ³ 2).
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Th 11/17/05
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HW due:
The STA Mathcross #2 is now available.
But before you work on that, your assignment is to write out—from memory, if
possible—the characteristics of a binomial distribution and of a geometric
distribution. Then categorize each of the following situations as binomial, approximately binomial,
geometric, approximately geometric, or none of these. Fill in the additional blanks as requested. No
work is required.
1. I will draw 15 cards without replacement from a standard, well-shuffled
deck. I am interested in knowing the probability distribution of the number
of red cards that I obtain. Category: ___________
2. Same as #1, except that I will replace cards and reshuffle the deck
between each selection. Category: ___________
3. Same as #1, except that I am interested in knowing the expected number of
cards I must draw in order to obtain a red card. Category: ___________
4. Same as #3, except that I will replace cards and reshuffle the deck
between each selection. Category: ___________
5. What is the expected number of cards I must draw in order to obtain a red
card in #4?
6. What alternate name do we give to the phrase “expected number of cards”?
__________
7. The incidence of HIV in the District of Columbia is approximately .015
(i.e., 1.5% of the population). In an SRS of 250 residents, I am interested
in the probability distribution of the number of HIV-positive people that I
will see. Category: ___________
8. Same as #7, except that the random variable of interest is the number of
positions down my list I must go until finding someone who is HIV-positive.
Category: ___________
9. I will roll a fair die in a fair manner, 100 times. I am interested in
knowing the probability distribution of the total value of the rolls (which
could range from a low of 100 to a high of 600). Category: ___________
9(a). The expected number of rolls needed in order to obtain the first ace
(i.e., 1 pip showing) is ___________ .
9(b). The expected number of rolls needed in order to obtain the first roll
that is a multiple of 3 is ___________ .
10. I will flip an unfair coin, weighted so as to have a 60-40 bias in favor
of heads, a total of 200 times. I am interested in knowing the probability
distribution of the total number of tails (which could range from a low of 0
to a high of 200). Category: ___________
10(a). The expected number of flips needed in order to obtain the first tail
is ___________ .
10(b). The expected number of flips needed in order to obtain the first head
is ___________ .
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F 11/18/05
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Quiz:
There will be a short quiz covering ideas from the last two days’ HW
assignments. For example, you may be asked to compute the probability of
obtaining more than 17 but fewer than 24 heads when flipping a fair coin 40
times. (Answer: 0.651. If you can’t compute that, I expect to see a detailed
explanation at the beginning of class concerning what you tried and where you
think you might have gone wrong.. “I don’t understand” does not qualify.)
One of the items on the quiz will be to list the characteristics of binomial
and geometric distributions. You need to be able to write these out cold,
without notes, in exactly two minutes. There are five items in each list if
you count (as you should) the description of what the meaning of the random
variable X is in each context. Use
ditto marks or the word “ditto” to indicate the three places where the
geometric setting is identical to the binomial setting.
HW due: Read the DUI
Hokeypokey article from Tuesday’s Post
and answer the following questions.
1. Did the researchers use a matched pairs design in testing the
effectiveness of the field sobriety tests? If so, what sentences in the article
reveal this? If not, do you believe a matched pairs design would have been
more effective? Explain briefly.
2. Of the many objections the article raises to the methodology used for
researching field sobriety tests, which do you think is the most damning?
Fun Friday: Time permitting, you
may work on the STA Mathcross #2 at the
end of class.
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M 11/21/05
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HW due:
Write a paragraph in which you propose an alternative methodology for developing
and evaluating field sobriety tests. Indicate where you would use blinding
and blocking techniques. (Matched pairs or triples would be an extreme
example of blocking. Other blocking techniques might include segregating
subjects based on demographic criteria that might introduce too much
variability in the data if we did not perform a “column differences”
technique as illustrated in class last Friday.)
Then, complete STA Mathcross #2 as a
real assignment. It has more educational content than you probably realize.
You may work with friends, parents, classmates, and even students in other
classes (e.g., AP Calculus AB).
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T 11/22/05
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HW due:
Complete STA Mathcross #2 (will be
graded today for completion). Perfection is not required; solid effort is.
Quiz on Sunday’s “Unconventional
Wisdom” may be followed by either Ask-Backward Bingo or the association game.
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Thanksgiving break.
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M 11/28/05
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No additional HW due.
However, equipment checks and spot checks of old HW assignments may occur.
Guest speaker: Dr. Mark Sullivan, full-time engineer in private enterprise
and adjunct professor at George Mason University, will discuss the statistics
behind GPS calculations.
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T 11/29/05
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HW due:
Read the GPS supplementary notes, and
rewrite your notes from yesterday’s class so that they are legible and coherent.
If you need to work with classmates to piece together a set of notes, that is
also fine. If you have a set of class notes, properly formatted with your
name and date, then you will receive credit for this assignment even if the
notes themselves are not in your own hand.
Quiz (10 pts.) will cover Dr.
Sullivan’s talk. Don’t worry about the formulas. The important facts are
mostly in what he said, not what he wrote on the whiteboard. Any handwritten notes you wish to use
during the quiz are acceptable.
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W 11/30/05
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HW due:
Answer the Monty Hall problem and the drawers problems.
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