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T
3/1/05
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HW due:
Read the PHA(S)TPC procedures.
Follow all steps to answer the following question:
Candidate Smith is running for re-election to the House of Representatives.
Her political consultant tells her that she now has a clear majority of the
likely vote, since the latest tracking poll shows her with 52% and her
opponent with less than a majority. Set up H0: p = .5
and Ha: p > .5 to see whether the
consultant’s conclusion is justified. Assume a significance level (P-value) of 0.05 and a random sample
of 1000 likely voters in the tracking poll.
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W
3/2/05
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HW due:
Apply the PHA(S)TPC procedures
to determine whether Milton (in our classroom example) has really improved his
mean bench press weight after his dietary change. Recall that the sample
means were 200 lbs. before and 205 lbs. afterward, with s.d. of 4.3 lbs. and
4.0 lbs., respectively. Sample sizes were 50 in each case. Show all steps,
especially the assumptions. For the assumptions to check, you will need to
read ahead in the textbook(s) or check the TI-83 STAT TESTS Summary.
Show all steps clearly except for the calculation of the degrees of freedom
and the P-value. For df, simply use
STAT TESTS 4 and record the value of df that your calculator gives you. For
the P-value, you can use tcdf to
check the value that your calculator reports as lower case p. (How confusing.)
Note: At one point, your calculator
will ask you whether you wish to use “pooled” procedures. The answer is
always no. The use of pooled procedures (technically called homoscedastic
procedures) is a leftover from the days when pooled procedures would simplify
the computations somewhat. However, pooled procedures require additional
assumptions regarding the populations, and these assumptions are usually not
justifiable. Moreover, with modern computers, the savings in computation time
is not really worth anything anyway.
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Th
3/3/05
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HW due:
This is a 2-part assignment.
1. Submit your conclusion from yesterday’s HW by e-mail for critique.
Deadline: 8:50 a.m.
2. Also look at the following problems in the Barron’s book. Except for #11
on p. 317, do not actually solve these problems. Simply write down the code
(2, 4, 5, 6, or “none of the above”) of the STAT TESTS command that you would
use on your calculator in order to solve the problem. If the answer is “none
of the above,” provide a short explanation. The first several have been done
for you as examples.
p. 340, Example 15.7: none of the above (uses LSRL t test, which we will study in April)
p. 317, #3: STAT TESTS 5
p. 317, #4: enter data in L1, then use STAT TESTS 2
p. 309, #17: STAT TESTS 4
p. 305, #2: STAT TESTS 2 (this is a question concerning Type I error; the
probability of Type I error always equals the P-value of the test)
p. 306, #4: _________________
p. 306, #6: _________________
p. 306, #7: _________________
p. 306, #8: _________________
p. 307, #9: _________________
p. 307, #10: _________________
p. 307, #11: (Actually answer this one.) _________________
p. 308, #12: _________________
p. 308, #13: _________________
p. 308, #14: _________________
p. 308, #15: _________________
p. 309, #16: _________________
p. 309, #18: _________________
p. 317, #5: _________________
In class: Discussion of the student
conclusions (all of which were incorrect to some degree) to the Milton
problem. This was a good learning experience.
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F
3/4/05
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No additional HW due. We
will cover yesterday’s HW in depth.
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M
3/7/05
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HW due:
Work a selection of problems from the Barron’s book, showing work and a time
log of at least 35 minutes. The advantage of using the Barron’s book is that all
the solutions are given; that way you can check your reasoning. Note: Be sure to do the work first! Do
not look at the answers first.
Suggested problems: All of those that were due last Thursday, plus #4 on p.
377 and #6 on p. 379. Note that the time limit for #4 is 13 minutes (19½ for
extended time), and the time limit for #6 is 25 minutes (37½ for extended
time). For multiple-choice questions, show your scratch work and allow 2¼
minutes each; extended time is just under 3½ minutes each.
In class: Review.
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T
3/8/05
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Test on Confidence Intervals, Hypothesis Testing,
and Type I Error.
Study hints:
- Remember that the probability of Type I error
always equals the P-value of
the test.
- Type II error will be covered later. There will
be no questions concerning Type II error on this test.
- You are responsible for questions involving
means (t procedures) as well
as proportions (z procedures).
In other words, you must know how to use STAT TESTS 2, 4, 5, and 6 for hypothesis
tests, and STAT TESTS 8, 0, A, and B for confidence intervals.
- For full credit, conclusions must be stated
using approved wording and in the context of the problem.
- An example of a conclusion to a confidence
interval problem using t
procedures: “We are 80% confident that the true mean number of lunch
skips is 17.3 ± 1.8.” (The m.o.e. is 1.8.)
- An example of a conclusion to a confidence
interval problem using z
procedures: “We are 90% confident that the true proportion of addicts
who have HIV is .232 ± .035.” (The m.o.e. is 3.5 percentage points.)
- An example of a conclusion to a hypothesis test
problem using t procedures:
“There is insufficient evidence (t
= –1.176, df = 15, P = .129) that
the true mean fill level of the bottles is less than 300 ml.”
- An example of a conclusion to a hypothesis test
problem using z procedures:
“There is strong evidence (z =
2.372,
 = .43, n = 200, P = .0177) that the true proportion of support for Candidate
Jones does not equal 35%.”
- Assumptions (as outlined on the TI-83 STAT TESTS Summary)
must be checked. See also p. 636 in the main textbook to see how the
assumptions regarding normal populations can often be relaxed if n is at least 15 or 40. You must
either memorize the assumption rules or create non-paper-based study
notes. There is no prohibition against storing the assumption rules in
your calculator. However, the students who have tried this in past years
did not fare especially well, since it took them too long to find the
necessary information. If you know what you’re doing, you can check and
document all the assumptions while your classmates are still fumbling to
press the right buttons. For today’s test, I will simplify your life by
providing you with a copy of the TI-83 STAT TESTS Summary,
but on future tests, you will need to devise a solution of your own,
using either your memory or your calculator.
- You need to notice whether one or two samples
are involved. Based on your responses to the problems last Friday, I
would say that this is not as easy as it sounds. Note: In a “matched pairs” design, use one-sample procedures
on the differences.
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W
3/9/05
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No additional HW due today.
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Th
3/10/05
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HW due:
Please work several problems in the Barron’s book related to Type II error
and power. (Use the index. For example, #25 and 26 on p. 311 and #32 on p. 373
would be good places to start. Complete explanations for the answers are
provided. You should show sketches and scratch work.)
Please inform me of any grade-related issues for the third quarter by no
later than noon today.
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F
3/11/05
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Day of rest (also last day
of third quarter).
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M
3/14/05
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Career Day (no class).
The BIG TRIG CHALLENGE in Room S
(originally scheduled for today, in celebration of Pi Day) has been postponed
because of a meeting. Because there are also meetings Tuesday, Wednesday, and
Thursday after school, rescheduling may be difficult. However, stay tuned for
more information.
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T
3/15/05
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HW due:
First, answer the following essay question. It will take you at least 20
minutes if you do it correctly.
Explain, using diagrams, how each of the following affects the power of a
test. (In each case, assume that everything else about the test remains
unchanged. Your diagram should show the sampling distribution of the statistic
of interest, assuming that H0 is true, an alternative sampling
distribution at some fixed distance from the first one, and a boundary line
that shows whether H0 will be rejected or not. In other words,
follow the chalkboard presentation style from last Thursday.)
(a) Sample size is increased.
(b) Population s.d. is increased.
(c) The a level (i.e., the P-value cutoff level for significance)
is increased from the usual value of .05 to something higher, such as .075.
(d) Probability of Type I error is increased.
(e) The testing procedure is changed from one-tailed to two-tailed.
Then, with any remaining time you have, work more problems in the Barron’s
book related to Type II error and power. (See instructions from last
Thursday’s calendar entry.)
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W 3/16/05
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Work more problems in the
Barron’s book related to Type II error and power. (See instructions from last
Thursday’s calendar entry.) Be sure to
keep a time log. Allow slightly less than 2½ minutes for each multiple-choice
problem.
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Th 3/17/05
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Repeat yesterday’s
assignment with a 35-minute time log. Show your scratch work for problems
that require computation (most of them do require some).
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F 3/18/05
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Last day of class before
spring break. Easy HW due: Stop by
my office immediately after lunch Thursday (or before school Friday) to check
out your copy of How to Lie with
Statistics, a book that you will be reading over the spring break. The
book is a quick read (about 1½ hours) but is a classic in the field. If you
wish to read some of it overnight, that is fine but is not required. If there
is some legitimate reason why you cannot come to my office to pick up the
book, send me an e-mail with a complete explanation in order to earn credit
for having tried.
In class: Derivation of an extremely important linear regression
relationship!
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Week
of 3/21/05
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No school.
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Week
of 3/28/05
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No school.
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