Monthly Schedule

(AP Statistics, Period B)

M 1/3/05

HW due: Group project (experimental design and execution). If you plan to turn this in later in the week, please contact me by e-mail to confirm your projected submission date. If all three groups are finished by the end of the day today, there will be no additional graded work this week.

 

T 1/4/05

Well, so far only one group has turned in a project. The other two groups need to run a pilot study today during B period so that the test subjects in periods E and F can be treated today and tomorrow. (Thursday and Friday must be held open for midterm exam review.)

Quiz today: One probability problem similar to Pan’s College Challenge from class yesterday.

No additional HW is due for the rest of the week. Please work on your group projects!

 

W 1/5/05

Quiz today: Washington Post health articles.

In class: Introduction to binomial random variables (Chapter 8).

 

Th 1/6/05

Midterm exam review.

 

F 1/7/05

Midterm exam review (continued).

 

M 1/10/05

Midterm Exam, 8:00 a.m.–10:00 a.m., Room S. Bring several sharpened pencils, your calculator, and spare batteries. Paper will be provided; do not bring any paper or notes. Just as on the AP exam, you will not be allowed to swap calculators during the exam, and if your batteries die, they die.

Preparation hints: Use the Barron’s review book for all the topics through Chapter 7 of your main textbook. Select a mixture of multiple-choice and free-response problems. Also review all your old quizzes and tests. To keep things clear, we will not have anything from Chapter 8 on the midterm exam.

Format of the midterm exam: Multiple choice for the first half, free response for the second half. You may use your calculator throughout, and the memory will not be cleared beforehand. A copy of the formula sheet that I distributed last week will be provided for your use. (You must use the copy that is distributed at the exam; you cannot use the copy that was distributed last week.)

A note on AP-style questions: I am planning to draw the majority of the midterm questions straight from the Barron’s review book. What makes the questions a bit tricky is that they usually involve two or more concepts. There won’t be much along the lines of, “Compute the IQR of the following data set.” A more typical question would be something like, “Compared with data set 1, data set 2 has (A) a higher mean and a higher IQR, (B) a higher mean but a lower IQR, (C) a lower mean but a higher IQR, (D) a lower mean and a lower IQR, (E) the same mean but a higher IQR.” Or, instead of asking what the definition of placebo is, the question might give you several experimental designs and ask you which one is most prone to misinterpretation of results, and why. Do you see what I’m getting at? I can’t say with any certainty whether you would find the midterm easy or hard based solely on how you did on the previous quiz and test questions. The best way is to try a couple dozen of the Barron’s questions and see how you do. (Answer them first, under time pressure. Then check your answers and score yourself.)


Formulas: Remember that several useful formulas are missing from the formula sheet. Here are some that come immediately to mind:

  • z = (x – m)/s
  • P(A Ç B) = P(A) · P(B | A)
  • P(A Ç B) = P(A) + P(B) – P(A È B)
  • 68% of normal data are in interval m ± s, 95% in m ± 2s, 99.7% in m ± 3s
  • residual = y – yhat
  • If X and Y are random variables, and c and d are constants, then the following are true:
    mcX = cmX (expected value of a scaled r.v. allows the scaling factor to be pulled out)
    md + X = d + mX (expected value of a shifted r.v. is simply shifted by that amount)
    mX + Y = mX + mY (mean of a sum equals sum of means)
    mX – Y = mX – mY (mean of a difference equals difference of means)
    scX = csX (s.d. of a scaled r.v. allows the scaling factor to be pulled out)
    sd + X = sX (s.d. of a shifted r.v. is completely unaffected)
    Var(X + Y) = Var(X) + Var(Y), provided X and Y are independent
    Var(X – Y) = Var(X) + Var(Y), provided X and Y are independent


Except for the last one, most of these are nothing more than “applied common sense.” The last one (variance of difference equals sum of variances if independent) is tricky because it is somewhat unexpected. In my experience, this is the one most commonly missed by students.

As we discussed in class, some of the formulas on the formula sheet are of little or no value. Knowing which ones to ignore is useful.

As promised, here are links to blank copies of your old tests and two of the more significant quizzes. Please note that the second portion of the first test was taken from a copyrighted source (by permission of the textbook publisher) and cannot be posted on the Web.

 

W 1/19/05

Classes resume. In the second semester, we will suspend (at least for the time being) the weekly Washington Post health section quiz.

In class: Group work to answer the multiple-choice exam questions 100% correctly.

 

Th 1/20/05

HW due: Read Barron’s pp. 167-172. We will try using the main text as a source of problems and the Barron’s book as our main text. Note, however, that there are several important things you must know:

 

1.         This is a bit like studying literature by reading CliffsNotes or SparkNotes. Yes, you get all the “content,” but you don’t necessarily get the context you need. For some people, this works fine; others may hunger for more examples or more perspective. Worse, they may not hunger even though they should. It’s the danger of not knowing what you’re missing.

2.         You must actually do the reading. You can’t reduce the reading requirement to zero. (Not even the folks at CliffsNotes have figured out how to do that.)

3.         Because you are reading a summary, each page, each paragraph, and each word carry more weight. There’s no skimming allowed. In fact, you might need to take 5-10 minutes per page just to make sure you get everything that’s there.

4.         If something doesn’t make sense, don’t stay quiet. Ask about it in class, or if you’re too bashful, then by all means see me in my office or Math Lab.

5.         Taking reading notes on a summary seems a bit pointless. Accordingly, I will dispense with the requirement that you make reading notes from the Barron’s book. However, there will be frequent pop quizzes to provide a continuity check.

 

I will be in the Math Lab after chapel today (until 3:00 p.m.) for those who need more instruction and practice on solving binombdf and binomcdf problems.

 

F 1/21/05

Quiz (10 points) on binompdf and binomcdf calculations. See the comment in yesterday’s calendar entry if you need additional practice, or send me an e-mail message. You will not be required to show work on this quiz.

HW due: Main text #8.27 through #8.34 (all).

Until further notice, bring the Barron’s book daily. If you copy the full setup of each HW problem into your paper, you may leave your main textbook at home. (In other words, you need to copy an abbreviated form of the question before you start working the problem. You should be doing this anyway, but now, if you fail to do it and leave your main text at home, you will not be considered to have all your required equipment.)

 

M 1/24/05

HW due: Read pp. 174-180 of the Barron’s book. Page 173 is also useful (especially the last paragraph at the bottom of the page), but it is a rehash of material we have already covered.

I really need to ask that everyone does the reading this time. Read every word very carefully.

 

T 1/25/05

HW due: Write #8.55, 8.56, 8.63, 8.64.

 

W 1/26/05

HW due: Modify your two most recent problem sets (#8.27 through #8.64) to make sure that every problem includes a P( ) statement in terms of a clearly defined r.v.

 

Th 1/27/05

Since not everyone understood yesterday’s HW assignment, we will try again. Make sure that every problem defines a random variable clearly (e.g., “Let X = # of heads when flipping a fair coin 20 times”) and includes a probability statement such as P(X ³ 12) = 1 – P(X < 12) = 1 – P(X £ 11) = . . . (or whatever).

During the next 2 weeks (approximately), we will try as an experiment to have frequent unannounced 10-point quizzes, with problems taken mostly from the Barron’s review book or a comparable source. Anything that has been covered so far during the course is fair game. If the experiment is successful, the scores will be retained; if not, they will be discarded and treated as a learning experience only. These quizzes will be in addition to the normal complement of announced quizzes, tests, and HW, all of which will continue to be scored.

 

F 1/28/05

HW due: #8.27 through #8.34 (all), 8.55, 8.56, 8.63, 8.64. No blanks or gaps are permitted. At a minimum, each problem must have a clearly defined r.v. and P( ) statement. See yesterday’s calendar entry for clarification.

I cannot believe (1) that as seniors, you need to be told that if you are unable to complete a HW problem, then you should seek help from me or a classmate, nor (2) that I am rewarding this disingenuousness by giving you no additional assignment for today. However, it seems to make no sense to press onward until people have made a solid “college try” at the previously assigned questions. Some of what I have seen so far falls short of the mark.

Incidentally, the phrase “college try” should indicate the level of effort that is expected in this or any other course covering college-level material.

 

M 1/31/05

HW due: #8.60, 8.61, 8.62, plus the following questions based on Stan Stanford’s pitiful plight:

 

Stan Stanford, an STA student, is a loser but an honorable young man. He has computed that the probability that any individual young lady at NCS will agree to attend the prom with him is 0.045. The probability is the same for all the young ladies that he might ask, since they all regard him with equal disdain. There are about 300 eligible females at NCS, and Stan plans to approach 30 of them, one by one. He will not ask anyone twice.

 

1.         How many can be expected to say yes?

2.         Is question #1 from a binomial setting, a geometric setting, or neither? Explain clearly in several sentences or bullets.

3.         Compute the s.d. of the number of NCS females who say yes.

4.         Being honorable, Stan has rethought this situation and has decided to attend prom with whoever first says yes to him. How many NCS females can he expect to ask?

5.         Is question #4 from a binomial setting, a geometric setting, or neither? Explain clearly in several sentences or bullets.

6.         Perform a calculator simulation to estimate an answer to #4. Write a paragraph of explanation, as well as a table in which you clearly indicate your raw data (i.e., random values drawn) and outcomes of each run. Perform at least 20 trials (i.e., 20 runs).

7.         Using the same raw data, estimate the s.d. of the number of NCS females Stan must ask in order to obtain an acceptance of his invitation.

8.         Compare your estimate of the mean in #6 with the true mean you computed in #4. How close did your simulation come?

9.         Compare your estimate of the s.d. in #7 to the true value found by formula. Indicate the source for your formula (Barron’s book, main text, Web page, library book, or whatever).

 

In class: Review for test. Answers to the Stan Stanford questions are now available.

 

 

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Last updated: 02 Feb 2005