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Th 2/1/07
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Optional Re-Test
(and Make-Up for those who missed Tuesday’s test), 7:05 a.m., Room R. Please arrive at 7:00 so that we
can begin promptly at 7:05. Extra-timers should arrive earlier than that.
Anyone who arrives after 7:10 will probably not have time to finish. If you
do well, the score on Wednesday’s test will be discarded.
HW due: Read pp. 472-479, including the summary; write #9.25. Note that
there is no need to compute the probabilities requested; you need only
explain why the methods of §9.2 cannot be used to compute those
probabilities.
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F 2/2/07
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No additional HW due. This is your golden
opportunity to plug the gaps on old problems, some of which may be randomly
re-scanned today.
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M 2/5/07
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HW due: Read pp. 491-497; write #9.45, 9.46. Today is a
normal class period in Room R. Anyone taking a cut or a skip today should
e-mail his or her HW by no later than noon today. Remember to put a double
underscore at the beginning of your subject line. In your e-mail, you may be
creative in your typographical approach. For example, here is how you might
write up #9.43 for e-mail:
9.43.(a) Since z=(x-mu)/sigma = (105-100)/15 = .3333, we have
P(WAIS
>= 105) = P(Z > .3333) = .369 by calc. [sketch omitted for e-mail].
(b) For an SRS with n=60, the mean
of the sampling distr. is still 100, but s.d.
(s.e.)
is greatly reduced, namely sigma/sqrt(n) = 15/sqrt(60) = 1.9365.
(c) Recalculate the z score based
on the reduced s.d. of 1.9365.
Instead
of getting z=(x-mu)/sigma = .3333 as in part (a), we have
z=(x-mu)/s.e.
= (105-100)/1.9365 = 2.582. Therefore,
P(mean
WAIS >= 105) = P(Z > 2.582) = .0049.
(d) (a) Answer could vary
dramatically if WAIS scores were non-normal, since
we cannot
calculate probabilities accurately for single-shot selections
without
knowing something about the shape of the underlying distribution.
(b)
Answers do not change, since formulas for mean and s.d. of the sampling
distribution
of xbar do not depend on the shape of the underlying distribution.
(c)
By the CLT, the answer should not change by much, since n=60 is a fairly
large
sample. Look at Example 9.9 on p. 490. Even with an extremely skew
underlying
distribution (Fig. 9.11a on p. 489), a sample of size 70 is large
enough
to overcome the problem of the skewness. Common sense tells us that
WAIS
scores would have much less skewness, and with n=60, we should have
a
large enough sample to make the sampling distribution of xbar be essentially
normal.
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T 2/6/07
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HW due: Listen to this
radio interview and be prepared for a Quiz on it. There is a lot of good statistical material in there.
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W 2/7/07
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HW due: Repeat #9.45 and 9.46 if necessary; write #9.44 and
9.47.
Hint for #9.44: Restate the probability
question in terms of the sample mean for a sample of size 12. In other words,
apply the hint found in #9.45(c) in a different context. Because this is a
standard AP-type problem, you need to be able to do it.
Hint for #9.47: If you try to answer
this using binomcdf, you may find (depending on what model of calculator you
use) that the calculator gags on the problem. However, even if your
calculator can handle the situation, I would like you to apply your rules of
thumb and restate the probability in question in terms of phat. As you check your rules of
thumb, you must state them and indicate that they are satisfied. Use a check
mark (ü)
to indicate that you have provided written verification, not merely that you
have looked at the situation. AP graders need to see evidence that you not
only know the rules of thumb but also are able to apply them. For example,
you might write the following:
N ³ 10n? Yes,
since N is theoretically infinite. ü
np ³ 10? Yes, since np
» n(phat) = 10,000(.5067)
= 5067 >> 10. ü
nq ³ 10? Yes, since nq
» n(1 – phat) =
10,000(.4933) = 4933 >> 10. ü
[The symbol >> means “much greater than.” This and many other symbols
and abbreviations can be found on Mr. Hansen’s
abbreviations page.]
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Th 2/8/07
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HW due
(optional): Read pp. 506-512. There
is no need for reading notes this time. Per our agreement, you cannot be
faulted if you skip this assignment, because it was not posted by 3:00 p.m.
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F 2/9/07
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HW due: Read pp. 506-518; write #10.1, 10.2.
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M 2/12/07
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HW due:
1. Enter the CINT program into your
calculator.
2. Write #10.6 (p. 519), with the modification that in part (a), you should
provide a normal quantile plot in addition to the requested stemplot or
histogram.
3. Write #10.8 (p. 520).
In order that you may know the level of detail that is expected, #10.5 is
done for you below as an example. Material within square brackets is
commentary for you and would not be expected to be included in the writeup.
We always need to check assumptions as listed in the STAT TESTS Summary.
10.5. [Check 3 assumptions: SRS, normal pop., known s.]
SRS? Not really, although
114/160 (71%) is considered an acceptable response rate. ü
Some
voluntary response bias is possible. Findings should be
interpreted
cautiously, since we do not have a true SRS. [For
example,
the longer-serving managers, having had more years to
master
the job, may be more likely to have free time and hence a
greater
willingness, on average, to respond. Or, you might speculate
that
the bias cuts the other way, with longer-serving managers being
successful,
goal-oriented people who would be more likely to view a
questionnaire
as a time-waster and discard it. Common sense tells us that
the
net bias coming from voluntary response here is probably small, but
without
additional data, there is no way to know for sure.]
Normal pop.? Doesn’t
matter, thanks to CLT. With n = 114
> 40, we should be safe.
[See
box on p. 606.] ü
Known s? Not realistic, since s is a parameter, hence never known. However,
s = 3.2 is given in the problem. ü [For a more realistic problem, we
should
treat s as unknown, compute s » s from the data, and proceed
with
the t procedures that were invented
by William Sealy Gosset
(a.k.a.
“Student”) of the Guinness brewery. However, that is a job for
another
day.]
s.e. = s/Ön = 3.2/Ö114 = .2997
z* = 2.576 [from Table C on p. 837 or, more conveniently, inside
the back cover]
m.o.e. = (z*)(s.e.) = (2.576)(.2997) = .772
C.I. = est. ± m.o.e. = 11.78 ± .77 years
alternate format
(optional): C.I. = (11.01, 12.55)
Conclusion: “We are 99%
confident that the true mean length of service is between
11.01
and 12.55 years.”
If you are given this problem on the AP free-response section, you need to
show the checking of the assumptions and the calculation of m.o.e. as shown
above. However, if you are lucky enough to get the question in the
multiple-choice section, simply follow the steps shown below.
STAT TESTS 7
Highlight “Stats”
Press ENTER
Set s to 3.2
Set xbar to 11.78
Set n to 114
Set C-Level to .99
Highlight “Calculate”
Press ENTER
That’s all you do! Then, if you desire the answer in “estimate ± m.o.e.” format, execute the CINT program before you do anything
else.
Similarly, you can double-check your answer to #10.6(b) by following these
steps:
STAT EDIT
Place cursor on L1 (not below, but directly on L1)
ENTER CLEAR ENTER (this is a quick way to remove all data from list L1)
Punch the 44 values from #10.6 into the list
2nd QUIT
STAT TESTS 7
Highlight “Data”
Press ENTER
Set s to 11
Set List to L1
Set Freq to 1
Set C-Level to .99
Highlight “Calculate”
Press ENTER
Press PRGM
While EXEC is displayed at top of screen menu, highlight the CINT entry
ENTER ENTER
Of course, for full credit, you need to show the checking of the three
assumptions (SRS, normal pop., known s) and the calculation of m.o.e., but at least now
you know what you’re shooting for!
For #10.6, checking the assumptions is faster than in #10.5. You may copy my
work from below if you wish:
SRS? Not stated. Must assume to proceed. ü [If sample is from one class (as in part (c)),
answer is worthless.]
Normal pop.? Not given, but NQP [see rough sketch from part (a)] shows nearly
a straight line. [Thus the sample
is nearly normal, and since this is a large sample (n > 40), that is good evidence that the pop. itself is
normal.] Besides, by CLT, sample is large enough that normality of the pop.
does not matter. ü
Known s? Not realistic [since s is a parameter], but s = 11 was given. ü [In the future, we will use t procedures in a situation like this. After you are 21, you may
even wish to celebrate the t
procedures by enjoying a pint of Guinness.]
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T 2/13/07
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HW due: Read pp. 520-528. The cautions on pp. 524-525 are
so important that you should read them at least twice. Then write #10.16ab.
For part (a), consider only whether the buttons have been pushed correctly.
Calculate your answer to the nearest dime, not to the nearest dollar as was
done in the textbook.
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W 2/14/07
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Ice storm (no school).
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Th 2/15/07
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HW due: Read pp. 531-536; write #10.18, and write one or
more research question proposals for your upcoming experimental project. Be sure
to phrase your idea in the form of a question (e.g., “Does male sweat affect
female hormone levels?”*), and do not recycle any of the ideas that were
discussed in class yesterday. One of your groups may still be able to work on
one of the ideas discussed yesterday, but you may not count those for
homework credit.
Group submissions are not permitted for this homework assignment. You must
work alone. Group work will begin next week.
__________________________________________________________
* Actually, it does. Check out the STAtistics Zone “Fun Links” section.
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F 2/16/07
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No school.
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M 2/19/07
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No school.
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T 2/20/07
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HW due: Read this
recent article from New York
magazine (dated 2/19/2007). I am indebted to a Lower School teacher who
brought this to my attention. I predict that this article will be much
discussed by your parents in the weeks and months ahead.
Answer the following questions:
1. Do you find Carol Dweck’s research findings conclusive? counterintuitive?
controversial? something else? What thoughts or feelings did the article
trigger in you? Write approximately one paragraph.
2. What additional information about Dweck’s methodology do you wish you had?
Write a short paragraph or bulletized list.
3. Think of a different experiment related to praise and achievement that you
could design and perform with relative ease, perhaps using STA Upper or Lower
School students as test subjects. Do not use one of the examples given in the
article. What would be your research question? What would be your methodology
(approximately one paragraph)?
4. Write #10.25 on p. 530. Show your work. (There is not much to show. Just
show the formula, plug-ins, and answer, except that instead of writing sestimate,
use the other notation we have discussed in class. You will not actually be
computing anything complicated, because you have already been given the value
for s.e. The answer given in the back of the book is correct, but you must
show your work in order to receive any credit.)
5. Explain why you could use invNorm(.975) to find the z* value you need in #10.25, but why you could not use
invNorm(.95). I am expecting a diagram plus a sentence or two.
If you do well on this assignment, I will praise you for thinking hard and for taking
the time and effort to do your homework. I will not praise you for being
smart.
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W 2/21/07
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HW due: Read pp. 537-549; write #10.39, 10.40.
Also, if you have not already done so, purchase the Barron’s review book (ISBN
0-7641-2193-6) and bring it to class today for an equipment check. I reminded
you last week that this textbook, which is on the required textbook list,
would soon be needed in class. The full title is How to Prepare for the AP Statistics Advanced Placement Examination,
3rd Edition. The editor is Martin Sternstein, Ph.D.
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Th 2/22/07
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HW due: Read pp. 550-556 and the PHASTPC handout. Learn the steps in
the handout by heart, and be prepared for a possible Quiz covering the names of the steps (in sequence) and the types
of issues that we discussed in class yesterday.
Extra credit if you come up with a
clever new mnemonic to replace Please Help All Students To Pass Calculus . .
.
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F 2/23/07
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HW due: Read pp. 560-562; write #10.58. Previously assigned
homework, including homework that has already been scanned, may be scanned or
collected today.
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M 2/26/07
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HW due: Read pp. 562-567. No additional written work, but please
make sure that you are caught up on the previously assigned problems. We will
have a massive HW scan this week.
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T 2/27/07
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HW due: Review your previously assigned problems from
Chapter 9, plus problems #10.77, 10.78, and 10.83 through 10.86 all.
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W 2/28/07
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Test on Chapter 9, plus §§10.1 through 10.3.
Important: Bring your HW binder so
that I can score your HW while you are working on the test. Make sure that all
your assignments (or at least the ones you have) are in chronological order
on 3-hole punched paper. I will scan an SRS of problems. If you are not
caught up on HW, do as many problems as you can (you should be doing this
anyway in order to prepare for the test), and hope for the best.
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