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T 2/1/011
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No additional HW is due
today, but older assignments may be rescanned. In particular, any answers
given in class or posted on-line should be correctly reflected in your HW
papers.
Yesterday’s tests were fine. There were no failures. The mean and median were
both 87, the standard deviation was 7, and although the tails were fat, there
was not any pronounced skewness. I see no compelling reason to hold a make-up
test today for the 3 students who requested a make-up, but if those students
will contact me individually, we can discuss the matter.
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W 2/2/011
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HW due: Read pp. 537-548;
write #10.36.
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Th 2/3/011
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HW due:
1. Read the 20 starred problems from the Must-Pass Quiz. Be prepared to
answer any of them, cold. When preparing, it is not considered cheating to
consult the answer key at the link that is posted there.
2. Correct yesterday’s assignment, using the answer key posted at hwstore.org.
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F 2/4/011
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HW due:
1. Read the PHA(S)TPC handout.
No reading notes are required for this handout.
2. Read pp. 550-558. Reading notes are required, as always.
3. Write #10.56a using the full PHA(S)TPC procedures. For now, it is
acceptable to jot the letters down to help prod your memory, just as long as
you omit them when you take the AP exam.
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M 2/7/011
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HW due: Read pp. 562-567
and the Study Guide below; write #10.62 using the full PHA(S)TPC procedures. If for some
reason (cough, cough) you are not able to attend today’s class in the
aftermath of Super Bowl XLV, you may submit this assignment for full credit
tomorrow.
There is a rumor that Mr. Hansen may be very lonely in class today . . .
Here’s an idea: Why not use the weekend to work not only on this assignment
but on tomorrow’s (longer) assignment as well? That would be a win-win for
everyone.
Study Guide
Mr. Hansen is frequently asked, “What, exactly, are the assumptions I need to
check?” For the two types of hypothesis tests we have looked at, the question
can be answered as follows:
1-prop. z test (STAT TESTS 5 on calculator):
1-sample t
test (STAT TESTS 2 on calculator):
- SRS
- [Unknown
 : no need to list or check this, since this is always
true in the real world.]
- Approximately normal population (see p. 553) or
 .
(Our previous textbook said this: If n
< 15, normality is required. If n
is between 15 and 40, normality is not required, but there must not be
any outliers or strong skewness. If  , even strong skewness is acceptable. If you find this
to be too complicated to remember, you may use our textbook’s
streamlined rule shown at the bullet above.)
Final note: Do not forget that a single extreme outlier (as described in The
Black Swan, an excellent though lengthy book by N. N. Taleb) can
completely invalidate a t test. You
may also find this
article to be interesting optional reading. Taleb made many millions of
dollars by buying what he perceived to be underpriced options related to
highly improbable “black swan” events. If that is something you would like to
do, maybe the next expansion of Marriott Hall can be named for you.
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T 2/8/011
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HW due: Read §10.6 (pp.
571-574) and the Summary of Key Concepts and Formulas (pp. 575-576); write
Activity 10.2 on p. 575, plus #10.80, 10.84, 10.90, 10.95.
Note: Because there are more
problems in this assignment, problems #10.80, 10.84, and 10.90 would take
quite a while if you did all 3 of them using full PHA(S)TPC procedures. Therefore,
you may do 2 of them (your choice) as “button pushers” if you wish. Show full
work on the other one.
Note: Since developing speed and
facility is part of what you need to practice, you may prefer to use
PHA(S)TPC throughout. That is certainly better, and maybe if you have some extra
time on Monday (cough, cough) you would be willing to do that, since it goes
beyond the minimum requirement and would help you to learn better.
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W 2/9/011
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HW due: Read pp. 583-597,
being careful not to learn the
formula for df that appears in the green box on p. 586 and the tan box on p.
587; answer the questions below.
1. Why should students avoid looking, even for an instant, at the 2-sample df
formula on p. 586 or p. 587? List as many reasons as you can.
2. Why will we never (and I literally mean never) use the pooled 2-sample t procedure described in the middle of p. 594?
3. At Southern North Dakota High, 32 public school students are given a
pretest on their knowledge of precalculus. Then, an expert teacher is brought
in to give them some remedial tutorials over the span of a week. At the end
of the week, the students are tested again. The 32 original scores are stored
in calculator list L1, and the 32 scores at the end of the week
are stored in list L2. Exploratory data analysis reveals that the
mean of the “before” scores is 48, with a sample standard deviation of 12.2,
and the mean of the “after” scores is 52, with a sample standard deviation of
9.8. The null hypothesis is that the true mean precalculus ability of the
students is unchanged, and the alternative hypothesis is that the students’
true mean ability level after the week’s training is higher than before. It
is generally considered valid to treat test scores as an SRS from the pool of
all possible test scores that these students could have earned. Explain why
it is not valid to punch the
following commands into a TI graphing calculator in an effort to find the P-value:
STAT, TESTS, 4, Stats, 48, 12.2, 32, 52, 9.8, 32,  , Pooled:No, Calculate, ENTER.
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Th 2/10/011
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HW due: Read pp. 606-614;
write the exercise below.
Here are the raw data from the Southern North Dakota High problem mentioned
in yesterday’s assignment. “Pretest” refers to the test that was given before
the expert teacher visited, and “posttest” refers to the test that was given
afterward.
Please answer the following questions.
1. Are the pretest scores normally distributed, skew left, or skew right?
Sketch a normal quantile plot to support your answer. If you have forgotten
how to make a normal quantile plot, which is understandable (since we learned
about NQPs last fall and have not done any recently), then you are expected
to relearn the subject by Googling and/or by reading the manual for your TI
calculator. If you have forgotten how to interpret your NQP, please reread
pp. 414-416 in your textbook.
2. Are the posttest scores normally distributed, skew left, or skew right?
Again, sketch the NQP to support your answer.
3. In class yesterday, we discussed how the proper way to approach this
problem (and all similar matched-pairs problems of this type) is to look at
the column of differences (i.e.,
the improvement that each subject seemed to experience). We will define the
difference to be posttest minus pretest. What does a negative
improvement indicate?
4. What does an improvement of 0 indicate?
5. Are most of the difference scores positive? How many are negative? How
many are 0?
6. Are the difference scores (posttest minus pretest) normally distributed,
skew left, or skew right? Sketch the NQP.
7. Compute the mean and s.d. of the difference scores.
8. By how many points, on average, did each student improve on the posttest?
9. Run a button-pushing 1-sample t
test on the column of differences. The null hypothesis would be that the true
mean improvement is 0, and the alternative hypothesis is that the true mean
improvement is positive. If  do we have evidence
that the true mean improvement is positive? Justify your answer by writing a
conclusion in context, with a P-value
in parentheses.
10. Now pretend that instead of giving a pretest and a posttest to 32
randomly selected students, SNDHS officials instead decide to run a true
2-sample experiment with independent samples. In other words, after 64 subjects
have been randomly divided into a “control” group and a “tutored” group, the
control group has raw data as shown in the first column above  and the tutored
group has raw data as shown in the second column above  Run a button-pushing
2-sample t test to see if there is
any evidence that the true mean score of tutored students is higher than the
true mean score of control students. Again, use and justify your
answer by writing a conclusion in context, with a P-value in parentheses.
11. What do these data illustrate about the value of blocking? (Remember,
matched pairs is like an extreme form of blocking.) Write a thoughtful
paragraph.
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F 2/11/011
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HW due: Read pp. 619-626 and
answer the questions below.
1. Now that you have heard a few good answers to #11 from yesterday’s
assignment, make a second attempt at answering the question. Regardless of
whether or not your answer yesterday was good, rewrite your answer today
using all of the following terms: independence,
variance/variation, experimental units, matched pairs/blocking, P-value, s.e.
2. Yesterday you computed the s.d. of the pretest scores and the s.d. of the
posttest scores. Use the formulas you learned earlier in the year to compute
the s.d. of (posttest − pretest) under the assumption that posttest and
pretest are independent random variables.
3. In a matched-pairs experimental design, are the samples independent?
Explain briefly why or why not.
4. Yesterday you computed the s.d. of the (posttest − pretest) column
to be 12.269 in the matched-pairs setting. Is this larger or smaller than the
answer you computed in #2?
5. Go back and edit your answer to #1 one more time. Try to incorporate what
you learned from questions 2, 3, and 4.
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Weekend e-mail
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Dear STAtistics Student:
If there was one message that came through loud and clear in your suggestions
on how to reduce the “cramming culture,” it was the idea of more frequent
low-stakes evaluation opportunities to help prepare you. Accordingly, we will
be having a half-period practice test on Monday.
I want you to take this seriously, even though it will not, technically,
count for a grade. Going into a practice test unprepared is no more helpful
to your learning than going into a real test unprepared, even though the
consequences to your grade are lessened.
You may be thinking, “How do I practice for the practice test?” You should
review, of course, but then you should do Monday’s homework under time pressure.
There are three problems (#11.64, 11.66, and 11.90 on pp. 634-641), and you
should allow 39 minutes for them when using full PHA(S)TPC procedures. Be
sure to score your work by using the key that will be posted by late Sunday
evening.
Then, if you want to assemble a longer practice test for yourself, all you
have to do is choose 4 problems at random from pp. 576-580 and 634-641. Set a
timer for 50 minutes. (Extra timers: 3 problems in 56 minutes.)
Sincerely,
Mr. Hansen
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M 2/14/011
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Half-Period Practice Test on Chapters 10 and 11.
HW due:
1. Read pp. 629-632 and the condensed
chapter summary for Chapter 11.
2. Write #11.64, 11.66, and 11.90. Note that #11.66 requires 2 sets of full PHA(S)TPC procedures; the others
are somewhat shorter. After doing the problems, correct your work by visiting
hwstore.org for the solution key
(posted at 4:00 p.m. Sunday). For full credit, you should make the
corrections before coming to class.
3. Prepare for today’s half-period practice test on Chapters 10 and 11.
I know what you’re thinking: “Will the practice test be graded?” The answer
is “No, but I hope that doesn’t give you the idea of postponing studying
until Tuesday night.”
Your excellent suggestions for reducing
the culture of cramming have convinced me that one thing I can do to help
you learn is to give you some low-stakes (but still timed) exercises so that
you know what to expect. The truth is, of course, that you could create your
own half-period practice test by randomly choosing any two questions from the
chapter review exercises on pp. 634-641. However, for reasons that I have
never understood, students seem to like it better when I select the questions
for them, and that’s what we will do today. You will be given two questions
to answer in 26 minutes. Full PHA(S)TPC procedures are expected.
After the practice test, I will distribute a scoring rubric. Your scores will
be recorded for information only (not as part of your grade average). As you
know, mid-quarter is almost here, which means that the score on the practice
test may be part of what gets reported to your parents. For example: “Your
son Johnny is enjoying his study of STAtistics and is participating well in
class discussions. He sometimes steers the discussion off topic, but everyone
enjoys his witty humor. Nevertheless, his extremely low score on the Feb. 14
practice test suggests that he is relying on a culture of cramming to pass
his tests. This is not a good strategy for college, since it predicts that he
will consume several hundred thousand dollars of your family’s money without
actually learning much of anything. He would do much better if he studied
thoughtfully each night, asked more questions in class, and built his
knowledge brick upon brick over a long period of time instead of trying to
cram the night before the test.”
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T 2/15/011
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HW due: Grade yesterday’s 26-minute practice
test (#11.70 and #11.74 on p. 637) using the solution key. Scoring is 4
points for your name, plus 6/6/12/6/6/12 for PHATPC steps in each question.
Partial credit is permitted; for example, 3 out of 6 if you get one
hypothesis correct and the other incorrect. The 12 assumption points are
allocated as follows: 4 for identifying the type of test, and the other 8
points prorated based on the number of assumptions that were properly stated
and checked. In #11.70, there are 2 assumptions to check, so that means 4
points each. In #11.74, there are 7 assumptions to check, so deduct 1 point
for each error and keep the change.
In #11.70, there is a maximum score of 24 points out of 48 if you used a
2-sample test instead of a 1-sample test. That is a serious error.
You are also expected to study in preparation for Wednesday’s test. That’s
right! Studying and test preparation should begin days before the test.
Bonus opportunity: There were
several typos on the hard-copy solution key distributed in class yesterday.
All have since been corrected on the web version. These typos are all
mathematical in nature, which means that the first student who finds them can
earn 1 point for each. E-mail submissions are preferred. If you can find only
one typo, that is fine—simply submit the one that you found. Good luck!
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W 2/16/011
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Test (100 pts.) on Chapters 10 and 11. The best preparation for this test would be to
select review problems at random from pp. 576-580 and pp. 634-641.
Odd-numbered ones are recommended, since you can easily check your answers.
Remember that full PHA(S)TPC
procedures are generally required. Pacing: 4 problems in 50 minutes.
(Extended timers: plan on doing 3 problems in 56 minutes.)
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Th 2/17/011
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HW due: Read pp. 647-653
(middle); write #3 and #4 from yesterday’s test.
These questions may be graded for accuracy as well as for completion. If you
receive help from someone else, you must document such help in writing.
Copying, however, is prohibited in all cases. It is one thing to share ideas
or check answers, quite another to make a copy of someone else’s work.
Copying is an honor issue.
Hint: Question #3 is a 2-prop. z test with hypotheses as follows:
H0:
proportions are equal
Ha:
psychics’ proportion is higher
However, #4 is not a 2-proportion
situation, since you do not have 2 samples. Instead, you are comparing the
psychics’ proportion against a fixed number, namely 1/3.
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F 2/18/011
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No school.
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M 2/21/011
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No school.
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T 2/22/011
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HW due: A minimal
assignment to celebrate the long weekend! All you have to do is click here and enter a score
of 4 for the 2/22 assignment. This will become our new procedure for logging
HW points.
Everyone except for Ousmane and Edward scored 4/4 on that assignment.
Remember, you can still earn up to 3.6 points out of 4 if you are a day late.
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W 2/23/011
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HW due: Answer the question
below by making an Excel spreadsheet with headings for observed, expected,
deviation, squared deviation, weighted squared deviation, and a sum formula
for the  statistic.
M&M’s® plain candies supposedly have the following color percentages:
24% blue, 20% green, 16% orange, 14% yellow, 13% red, 13% brown. A fellow
named Josh
Madison, who apparently had way
too much time on his hands, counted 2620 M & M’s to test the color
distribution of the marketed product. Mr. Madison observed the following
counts:
481 blue
483 green
544 orange
369 yellow
372 red
371 brown
Run a goodness-of-fit test of the following hypotheses:
H0: pblue = 0.24, pgreen
= 0.20, porange = 0.16, pyellow = 0.14, pred = 0.13, pbrown = 0.13
Ha: Not all proportions
are as claimed.
Written work consists of a printout of your spreadsheet, showing the columns
as listed at the top of the assignment, the value of , and the P-value
of the test. Full PHA(S)TPC procedures are not required for this exercise.
Alternate assignment: If you do not have access to Excel, you can still earn
4 points by bringing in at least 2 small packs of M & M’s plain candies (not
Fun Size, but the standard retail-size packs). However, you must bring the
candies to class in order to qualify. If you miss class, you need to do the
Excel-based assignment above.
When you have finished the assignment, log your points by visiting the link
at the top of the schedule. Ousmane and Edward should also log yesterday’s
points (maximum of 3.6).
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Th 2/24/011
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HW due: Read pp. 653-656,
660-668; write #12.7abc on p. 658. When finished, remember to log your
points.
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F 2/25/011
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HW due: Read pp. 669-671,
677-680, and summary on p. 681; write #12.42, 12.46, and the crime problem
below. Then, log your points!
Problem:
The test for
independence is often used with an SRS that has been sliced up by two
categorical variables. However, it is also valid to use the test for
independence in situations where an entire population has been sliced in this
way. Consider the made-up data presented in class yesterday for a population
of 1000 crimes subdivided by category and age of perpetrator:
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< 10
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at least 10 but < 21
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at least 21 but < 31
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 31
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underage drinking
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5
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60
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0
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0
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[redacted]
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0
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50
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150
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420
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robbery
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13
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52
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200
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50
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(a) Compute the marginal totals, and verify that the grand total is 1000.
Cross-check the grand total.
(b) Prove, in writing, that the assumptions are met
(all expected counts 1, no more than 20%
of expected counts < 5). You can use your calculator to compute the
expected counts, but you must show the work for at least 2 of the cells.
(c) Conduct a complete PHA(S)TPC test for independence. [Actually, you are
allowed to omit the “Define Parameters” step for 2-way tables, since nobody
expects you to define all the conditional probabilities. There are 12
conditional probabilities in this problem, and if we needed to, we could
subscript them by row and column as follows: p11, p12,
p13, p14, p21, p22,
p23, p24, p31, p32,
p33, and p34.]
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M 2/28/011
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HW due: Read pp. 689-695,
omitting green box on p. 695; write #12.47 using PHA(S)TPC and redo #12.46b
(think hard!). Then log your points.
In class: An SRS of students will have their notebooks collected and audited.
If you are selected and have forgotten your notebook, the score is treated
similarly to an equipment check: 0 out of 4 points. If this happens to you,
you will also be first in line for the next audit.
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