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Th 11/1/07
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HW due: Read pp. 218-226; write #4.25, 4.26, 4.28, 4.50.
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F 11/2/07
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No
school (teacher work day).
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M 11/5/07
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HW due: Read pp. 245-252; write #4.46, 4.62, 4.65, 4.66.
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T 11/6/07
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HW due: Read pp. 253-268.
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W 11/7/07
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HW due: Read pp. 269-276; write #5.27, 5.28. In your reading
notes, see if you can predict what Mr. Hansen thinks is the single most
important concept in the reading.
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Th 11/8/07
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HW due:
1. Write the following definitions. (Copy them.)
statistically significant effect or
difference = an effect or difference that is too large to be plausibly
attributed to chance
P-value = probability that, if the
experimental and control group were identical in all respects and chance
alone were the only force at work, an effect as extreme (or more extreme
than) the observed effect might occur
alpha level (a level) = cutoff value for P,
i.e., the point at which we begin to think that statistical significance is
present
For example [write this also], Mr. Hansen said that flipping 4 heads in a row
does not seem to be statistically significant, since P = 1/16 = 0.0667. However, flipping 5 heads in a row is a bit
more impressive, since P = 1/32 =
0.0333. By tradition, although there is no mathematical basis for this, a is often taken to be 0.05.
2. Apply the concepts of control,
randomization, and replication to your group’s proposed project. Note:
This is an individual assignment, not a group assignment. Explain precisely
how each principle applies to your situation. If you do not remember what
your proposal was, then contact your group leader and ask. Example:
Control: We will, of course, have a
control group. We will go beyond that, however, to try to control as many of
the lurking variables as possible. For example, the person who says, “Very
good! You must be really smart!” will not always be the same researcher. We
will use all three researchers in all three roles, randomly chosen, so that
the researcher’s temperament will not be a lurking variable in the children’s
performance. We will also try to select children who are all in the same
grade level and of similar ability levels so that there is not much
variability in IQ among the subjects.
Randomization: We do not
need an SRS of schoolchildren. Not only is such a sample impractical to find,
but it would be unethical to force randomly chosen schoolchildren scattered
across America to participate in our study. (It would also be prohibitively
expensive to fly them and their parents to Washington.) Instead, we will use
a pool of Beauvoir volunteer subjects. The choice of whether a child is in
the “Very good! You must be really smart!” group (group A), the “Very good!
You must have really worked hard!” group (group B), or the “Very good!” group
(group C) will be made by a random number generator using the following
protocol: 1. The integers 01 through 45 will be assigned to the 45 test
subjects. 2. A list (in L1) of numbers 01 through 45 will be
paired with a list (in L2) of 45 random real values. 3. We will
sort L1 using L2 as the sort key. The command for this
is SortA(L2,L1). 4. After sorting, the first 15
students who are at the top of the sorted list will be assigned to group A,
the next 15 will be assigned to group B, and the remaining ones will be
assigned to group C.
Replication: We will double-check
with Mr. Hansen, but we think that 45 test subjects will be enough to
demonstrate that our findings are statistically significant, not simply the
result of “flukes” in the children themselves. For example, even if there are
6 exceptionally high-IQ children who might skew the results, it is unlikely
that all 6 would end up in the same treatment group.
Note: If we have reason to believe
that the IQs of the children have a high s.d. or are bimodally distributed,
we should revisit the “Control” section above by blocking on IQ (perhaps
using low and high IQ as the blocking criteria) and recruit enough subjects
so that there are at least 10 subjects in each block for each of the
treatment groups (A, B, C). Since this would require a minimum of 60 subjects
(2 times 3 times 10), we would probably need to recruit about 90 to be safe.
The rule is “BLOCK FIRST,” which would make our experimental design look like
this:
3.
Prepare for the “Quick Study” quiz that was postponed from yesterday.
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F 11/9/07
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Big HW due: Since we did not get to the Quick Study yesterday,
please submit the following take-home quiz in your own handwriting.
Legibility, grammar, and clarity of thought are all counted. Because this is
a fair amount of writing, the score will be much higher than the usual 4
points given for homework. You may discuss answers with friends, but all
writeups must be in your own handwriting and in your own words.
1. What vocabulary term beginning with the letter M (not found in your
textbook) applies to the type of research described in the first article, the
one about stretching?
2. Suppose that you are a fitness guru whose mindset is that stretching is
valuable. Write a short paragraph that supports your position by citing the
article about stretching.
3. Suppose that you are a fitness guru whose mindset is that stretching is of
no value. Write a short paragraph that supports your position by citing the
article about stretching.
4. Is there evidence that Zometa causes
a reduction in risk of having one or more fractures? Why or why not?
5. Is there evidence that Zometa causes
a reduction in mortality risk? Why or why not?
6. Which is more statistically significant: Zometa’s result with respect to
fractures, or Zometa’s result with respect to mortality? Explain your answer.
7. Did the final study show that weight gain causes an increased likelihood of breast cancer? Why or why not?
8. List several (that means 3 or more) lurking variables that could play a
role in the perceived association between weight gain and breast cancer. Your
list should consist of the actual variable names. In a column to the right of
the variable names, explain each one with at least a sentence. Try to find at
least one lurking variable that “cuts the other way,” i.e., that would tend
to make women who had gained weight less likely to contract breast cancer.
Bonus points will be available if you find more than 3 good entries.
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M 11/12/07
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FLASH UPDATE! The assignment listed below has been postponed
until Tuesday in celebration of the Bulldogs’ 11-7 victory over the Landon
Bears in Saturday’s IAC championship football game. If you wish to work ahead
a day, you may—or you can enjoy a pleasant weekend of relaxation and
celebration.
HW due: Read pp. 277-281 plus the
summary on pp. 283-284; write #5.44. I recommend that you do the reading
assignment twice. Seriously! This is some of the most difficult material for
students to comprehend, perhaps because it seems relatively simple. The
assignment is short enough that you will have plenty of time to read your
pages twice. Remember to read all the examples as well (5.13, 5.14, 5.15, and
5.16).
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T 11/13/07
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HW due: No additional HW due, but make sure you have
finished the assignment listed in yesterday’s calendar entry.
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W 11/14/07
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HW due: Read pp. 286-296 and prepare a set of procedures
for simulating the birthday paradox with 30 people in the room. (In other
words, describe a procedure for estimating the probability that 30 strangers
will have a birthday in common. Ignore leap years, and assume that all other
days of the year are equally probable. Do not actually compute the
probability.) Also prepare for your “Quick Study” quiz as usual.
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Th 11/15/07
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HW due: Read pp. 296-300 (section summary and chapter review);
write #5.67, 5.72, 5.74.
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F 11/16/07
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HW due: Write #5.79, 5.81. I recommend that you use a
spreadsheet to do #5.79. If you do not know how to use a spreadsheet, then a
careful description of your methodology will suffice. For the #5.81, however,
use your calculator and actually perform the simulation to estimate the
probability in part (b).
In class: Review for test.
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M 11/19/07
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Test
focusing on Chapters 4 and 5 (100 pts.). The concepts of influential
observation and regression outlier
may also be tested, since they were not sufficiently covered previously. Also
note that terminology from earlier in the course (e.g., parameter, statistic,
sample mean, population, sample proportion, range, IQR, variance, r, r2,
sample size) will be fair game throughout the year and may appear on any
test, including this one.
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T 11/20/07
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HW due: Read pp. 310-329. Reading notes are required, as
always.
In class: Brief discussion of probability. The majority of the period will be
reserved for our guest speaker, Mr. Joe Morris, STA ’62.
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M 11/26/07
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HW due: Get lots of sleep! Record your number of hours of
sleep each night for a data-gathering exercise. (Estimates are acceptable.)
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T 11/27/07
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HW due: Read pp. 321-338; write #6.22, 6.28.
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W 11/28/07
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Penultimate
“Quick Study” Quiz (10 pts.) + HW due:
Read pp. 341-349; write #6.42. Table 6.1 is found on p. 347.
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Th 11/29/07
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HW due: Read pp. 351-355 + review on p. 359; write #6.54,
6.65 (tree diagrams required for both), plus the following four problems.
6.67
You have two fair dice, one red and one green. You shake them thoroughly and
roll them on a flat surface. Compute
(a) the probability that the green die shows an even number
(b) the probability that both dice show an even number, given that the red
die shows an even number
(c) the probability that both dice show an even number, given that at least
one of the dice shows an even number
Hint: Use the conditional
probability formula, being careful not to let common sense mislead you.
Common sense, after all, would say that all three answers are .5, and that is
not true.
6.68
You have a chest of drawers that has 3 drawers. There are 6 coins, 3 gold and
3 silver, that are placed in the drawers in such a way that one drawer has 2
gold coins, one drawer has 2 silver coins, and one drawer has both a gold
coin and a silver coin. The order of the drawers is then randomized, but the
contents of the drawer remain unchanged (one drawer with GG, one drawer with
SS, and one drawer with a coin of each type). You reach into the top drawer
and fumble around, blindfolded, for the two coins that are there. You select
one of them at random. What is the probability that the other coin in the
drawer is gold, given that the one you selected at random is gold?
6.69
You are a contestant on a game show that has the following rules. The emcee
has hidden a valuable showcase prize behind one of 4 doors. The other 3 doors
have nothing behind them. (In the original game show, Let’s Make a Deal, there would usually be a goat or some other
barnyard animal as a “joke” or “dud” prize behind the losing doors.) You will
be allowed to choose any door that you wish, but before it is opened, the
emcee will reveal 2 other doors that have no prize. The emcee can always do
this, after all, since regardless of whether your initial choice was correct,
there will always be at least 2 doors that can be opened without revealing
the prize. Clearly, at this point, the prize is located either behind the
door you initially chose or behind the other remaining door.
(a) What is the probability that the prize is behind the other remaining
door?
(b) If you are given the opportunity to switch, should you switch, or should
you stay with your original choice? Does it matter?
6.70
On Howie Mandel’s show, Deal or No
Deal, which airs next on 11/30/2007, there are a number of briefcases
held by attractive female models. If you are not familiar with the rules,
click here.
Use the language of our course to explain why the Banker’s offers are low if
a preponderance of high prizes have already appeared among the open
briefcases, but the offers are much higher if a preponderance of low prizes
have already appeared among the open briefcases.
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F 11/30/07
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Guest
speaker: Mr. Steven Berlin
Johnson ’86 will discuss “The Classroom of the Future.”
HW due:
1. Skim this
article about cell phone use and accident rates. The article is too long
to read in one evening, but be sure to read the executive summary carefully,
as well as all the graphs and tables, especially the graph on p. 39 that
shows the fatal accident data for Washington, DC.
2. Then read the comments
that bloggers and other interested parties have submitted. There are 17
comments. For each comment (please number them 1 through 17), indicate each
of the following to the best of your ability:
- Whether the comment is based, in whole or in
part, on anecdotal data (Y or N)
- Whether the writer seems to agree with (A) or
oppose (O) the authors of the article
- The writer’s overall skill at writing, on a
scale of 0 to 4 (0=illiterate nincompoop, 4=Ms. Denizé)
- The writer’s apparent knowledge of the subject
of statistics (0 for completely clueless, 4 for highly knowledgeable on
the subject)
For example, your data should be formatted something
like this:
1. YO44
2. NA32
3. YA04
[etc.]
Clearly, you will have to guess in some cases, and it may not be obvious how
you should guess. Make an intuitive leap, even if it is not fully justified
by rational criteria. Do not leave any entries blank.
Send your data to me by e-mail (modd [at sign] modd.net) so that I can
compile a spreadsheet. I am trying to keep spambots from scraping my e-mail
address from this web page. Be sure to put two underscores ( __ ) as the
first two characters of your subject line so that I know you are a STAtistics
student and not an evil spammer.
3. In class next Tuesday, Charlie will be betting dimes that his idea of
always going with his initial guess in the game show problem is a good idea.
To make this a sporting contest, I will pay him 2:1 odds (i.e., 2 dimes every
time he is right, but collecting only 1 dime from him every time he is
wrong). How much money can I expect to win from him if we play 10 rounds,
which is probably about all we will have time for?
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