Welcome to the STAtistics Zone

(Statistics, Period D)

Are you nervous when you see NCWEE? concerned when you see CIRC? perturbed when you see PBC? Visit Mr. Hansen’s fabled abbreviations page to make sense of those cryptic markings you see on your papers.


Schedule at a Glance (see archives for older entries)
Written assignments should follow the HW guidelines.
Recurring Assignment: Each Wednesday from 9/12/2012 through 12/5/2012, there may be a discussion or a graded open-notes quiz on the most recent “Quick Study” column in the Washington Post Health section.


M 2/11/13

HW due: Write #9.30 (using sketches for each—do not write tcdf even though that’s what you will use), 9.31, 9.32, 9.34, 9.40, and 9.42 on pp. 505-507.


T 2/12/13

HW due: Review problems, minimum of 35 minutes’ worth. Log your time and bring written evidence of what you worked on. Hashing through previously assigned problems is permitted, but use a fresh sheet of paper with Tuesday’s due date. Label the page number and problem number for each problem that you work on.

In class: Review.


W 2/13/13

Test (100 pts.) on Sampling Distributions, t and z models, Confidence Intervals, and Assumptions. This will be a 40-minute test, since a Friday schedule is in effect.

You will be provided with a standard AP formula sheet. A graphing calculator is required, and spare batteries are strongly recommended. A spare calculator is permitted. If your calculator conks out or locks up during the test, you may not borrow another.


Th 2/14/13

HW due: Write Activities 9.3 and 9.4 on p. 516.


F 2/15/13

No school (faculty professional day).


M 2/18/13

No school (holiday).


T 2/19/13

HW due: Correct last week’s test. Students with scores below 80 need to print out a fresh copy of the test and fill in everything, even questions that were correct on the first effort. Those with scores of 80 or above can simply write out corrected answers (for missed problems only) on a fresh sheet of paper.

Comparing answers with friends is permitted, but please use your own wording and your own style of presentation in the longer questions. Otherwise, you won’t learn much.

Presentation standards for the corrections will be at a higher level than they were for the original test, since you have more time. Cryptic work is not acceptable. Make your meaning clear!

IMPORTANT: Turn in both your corrections and the original test.


W 2/20/13

HW due:

1. Read the PHASTPC handout and memorize the 7 steps.

2. Write #10.89 on p. 579, using the PHASTPC procedures. Show all steps.

3. Write #10.72 on p. 576, using the PHASTPC procedures. Show all steps.


Th 2/21/13

HW due:

1. Make sure yesterday’s HW is fully corrected. If it is collected a second time, perfection is expected.

2. Write #11.81 on p. 639, using the PHASTPC procedures. Show all steps.

3. Write #11.80 on p. 638, using either the PHASTPC procedures or the abbreviated PA*MC procedures for confidence intervals. Show all steps. Note: The final question is really asking, “Is there evidence that the true proportions of decayed teeth are different?” (The question of whether the C.I. excludes 0 as a likely value is equivalent to asking whether there is evidence of a difference.)

4. Write #11.70 on p. 637, using the PHASTPC procedures. Show all steps.


F 2/22/13

HW due: Write #11.62 on p. 635, #11.66 on p. 636, #11.74 on p. 637. Use PHASTPC procedures throughout, and show all steps. Liberal usage of ditto marks is permitted, as long as your meaning remains clear.


M 2/25/13

HW due:

1. Write #11.52ab on pp. 627-628, showing work in the checking of assumptions and calculation of the C.I.

2. Write #11.84 on pp. 639-640. Use full PHASTPC procedures.

3. Finish Friday’s assignment. (You should have enough time.)


T 2/26/13

HW due:

1. Write #12.1 and #12.2 on pp. 656-657. Be sure to explain your answers (stating the df value) in all parts of #12.2.

2. Make sure that all previously assigned problems are neat, complete, and ready to hand in if necessary. You should have ample time tonight to work on older problems.


W 2/27/13

HW due:

1. Pick your favorite 5 projects, in order, from the list of research questions. Simply write down the ID numbers of your favorite, second favorite, third favorite, fourth favorite, and fifth favorite. Note that the ID numbers are not the same as they were yesterday in class.

2. Number your HW paper from 201 to 222. For each of the 22 proposed research projects, write the name of the statistical test (1-sample t, 1-prop. z, 2-sample t, 2-prop. z,  g.o.f.,  2-way, or LSRL t-test) that would probably be appropriate. In some cases you will have to do some educated guesswork, because the statement of the research question does not give sufficient detail. Be prepared to defend each choice. Use the ID numbers from the list of research questions.


Th 2/28/13

HW due: Each group must submit a draft methodology statement. Describe your method of selecting your sample, your target sample size(s), the data collection procedure in detail, and the type of statistical test you will use (including, if possible, your null and alternative hypotheses). Perfection is not expected on this draft. However, you must make a serious attempt.


F 3/1/13

HW due: Each group must submit a revised draft methodology statement. For full credit, the format must include names (spelled correctly) in the upper right corner, with group leader underlined or marked in some fashion, and with the palindromic date 3/1/13 featured prominently. (A student pointed out that there are also 10 more palindromic dates later in the month.)

Important: Explicitly show how the issues of control, randomization of assignment, and replication have been addressed. Randomization of selection of subjects is not particularly helpful for these projects.


M 3/4/13

HW due: Second revised draft methodology. Make sure that your methodology addresses all reasonable questions that people could ask about how you intend to carry out your project, and especially make sure that the research question and the rest of the methodology are consistent.


T 3/5/13

No class (Diversity Day).


W 3/6/13

No school (snow day). Thursday’s assignment was supposed to be posted by noon today, but since it was not, you can enjoy the Complete Snow Day Experience. Hurray!


Th 3/7/13

School resumes, presumably. No additional written work is due today.


F 3/8/13

HW due: Final revision of methodology. Remember, the goals of control, randomization of assignment, and replication must be explicitly addressed. That means subheadings! It is not enough to sprinkle these ideas here and there throughout your writeup. Subheadings will make your job easier.


M 3/11/13

HW due: Read the paragraphs below. Read them several times, and make some sketches to demonstrate that you have read them. Then write #12.9, 12.11, 12.14 on pp. 658-659, plus #12.19 and 12.20 on pp. 672-673. Use full PHASTPC procedures throughout, but you may use “. . .” to omit most of the tedious computations of the  statistic. When checking the size of the expected cell counts, you need to list all of the expected counts, but you do not need to show the work. With practice, you can do these in about 5 minutes each.

Reading assignment:

Power (statistical power) is the complement of  the probability of Type II error. (Remember that  the alpha-level of a test, is the probability of making a type I error.) If we are given  we can easily compute power as  since by definition, any two probabilities that are complementary must add up to 1. Duh!

Unfortunately, life is rarely that simple. Power calculation is challenging, and that’s all there is to it. The reason is that  is defined as P(failing to reject H0 | H0 false), but there are infinitely many ways in which H0 could be false! There is no way to come up with a value for  unless we consider one particular scenario in which H0 might be false, i.e., some plausible ES, and then see how much of that scenario’s sampling distribution would bleed into the “fail to reject” zone for the H0 sketch that we made in the PHASTPC process.

That is why we say that there is no single value for  and hence no single value for power. What we say, instead, is something like this: “The power of the test against an ES of 4.5 is 70% when we use ” Or, we might say something like this: “Our test has at least 65% power against each of the proposed values of the alternative, when

Pound this into your brain:  is the amount of the Ha (alternative) distribution that bleeds into the “fail to reject” zone.

Say it again:  is the amount of the Ha (alternative) distribution that bleeds into the “fail to reject” zone.

One more time:  is the amount of the Ha (alternative) distribution that bleeds into the “fail to reject” zone.

Make a rap tune out of it:  is the amount

(thump, thumpa, thump)

of the Ha (alternative) distribution

(thump, thumpa, thump)

that bleeds into the “fail to reject” zone.

OK, and power is just 1 minus . In other words, power is the amount of the Ha (alternative) distribution that stays in the “reject” zone. Do you see why power is called power? If H0 is false, we say that our statistical test has power if it can correctly identify that falsehood, which means that we would want to reject H0 if we could. However, we will reject H0 only if our test statistic falls in the “reject” zone, which it may or may not do, even if the null hypothesis is false.


T 3/12/13

Project list as of 3/11/2013:

Group 1 (Art Backstory): 2-prop. z, 2-tailed, fully randomized design
Group 2 (Headphones): 2-prop. z, 2-tailed, fully randomized design
Group 3 (Power Balance™): 2-sample t, 1-tailed, fully randomized design
Group 4 (Mental Math): modified  indep. test (right/wrong vs. time of day), same subjects used 4 times
Group 5 (Apple Juice): 2-prop. z, 1-tailed, fully randomized design

HW due: Answer the questions below for the “Art Backstory” 2-prop. z test, and then mimic the same 9-question process for one other project of your choice. (The second project can be your own, unless you are already part of the the “Art Backstory” project, in which case you will need to use one of the others for your second project.)

Let’s be clear about this: When you are finished, you should have 2 sets of answers, each numbered 1 through 9.

Given: Group 1 asked us to define p1 as the true proportion of people who prefer art when it has a backstory, and p2 as the true proportion of people who prefer art when there is no backstory.

1. What is the statistic whose sampling distribution we sketch when we are imagining the H0 sampling distribution scenario? Hint: It’s a little more complicated than  or .

2. State the null and alternative hypotheses. Use correct notation.

3. What model (z, t, or ) is being used for the sampling distribution? Are there any issues with the appropriateness of this model? If so, discuss briefly (1 sentence).

4. List the assumptions, and discuss whether they are likely to be met or not. For any that are violated, discuss the severity of the violation. Note: For now, you will have to estimate the sample size(s) used in your experiment.

5. For the statistic of interest (see your answer to #1 above), estimate a believable value for the ES. Use correct notation. What is your basis, if any, for this estimate?

6. Sketch the sampling distribution assuming H0 true, and then, using a different color of ink, the sampling distribution assuming that H0 is false in the particular way listed in #5.

7. State the  value you intend to use. If the value is different from 0.05, explain briefly why you chose that alternate value.

8. Calculate the boundaries between the “reject” and “do not reject” zones. Show your work. Mark these boundaries clearly on your sketch. Note: In order to do this, you will need to calculate the standard error, and in order to do that, you will need some additional estimates of s, p, or q. Provide a few words of explanation for how you came up with these.

9. Based on your sketch, what do you estimate is the power of the test against the scenario you estimated in #5?

Now, draw a thick horizontal line across your paper. State the short title and group number you wish to consider for your second set of answers, and repeat #1-9 above for that other project.


W 3/13/13

HW due: Produce a group document (with buy-in from each member) in which you estimate the power of your test against a likely alternative hypothesis. This will be a unified document in which you all agree on the methodology, the estimate of the ES, the estimate of s (if applicable), the  level, and the suitability of the power. Your goal for power is 70% or better. If you fall short, be sure to discuss the ways in which you could modify your project in order to increase the power of the test. It would be a shame to do all that work, only to find that your experiment was inconclusive on account of low power!

Your document will be collected at the start of class. If it is acceptable, you may begin data collection later today (Wednesday).

In class: Detailed discussion of older HW problems.


Th 3/14/13

HW due:

1. Begin working on your project if possible. If there is some logistical reason why you cannot begin just yet, that is acceptable. Group leader (or a deputy) must give a quick verbal project update in class today.

2. If you have not already done so, finish the 5 problems that were due on Monday 3/11.

3. Write #12.24 on pp. 673-674.


F 3/15/13

HW due: Work on group project, and be prepared for a quiz over all recent material.


M 3/18/13

HW due: Work on group project.


T 3/19/13

HW due: Draft (not final version) of group project writeup. All you are expected to have at this point is a table of raw data, in Excel format, and a short sketchy discussion of your research findings. You should be able to tell the rest of the class whether your research question was corroborated or not.

If it is not possible to run your real experiment just yet, then run a small pilot project.

In class: Discussion of methodology “lessons learned.”


W 3/20/13

Quiz (10 pts.) on all recent material.

HW due:

1. Read through p. 723 only. The remainder of the book is optional material that we may or may not do after the AP exam.

2. Write #13.28abcd on pp. 723-724. Note that the data table extends across the page break.

3. Provide a scatterplot with LSRL overlaid as part of your solution to part (a).

4. In part (d), remember to provide evidence
      (1) that the true fit is linear (check r2, scatterplot, and residual plot),
      (2) that the fit does not get worse as x changes, and
      (3) that the residuals are normally distributed.

Note: Your book talks a lot about “standardized residuals,” but don’t worry about those. We will use ordinary residuals throughout.


M 4/1/13

Classes resume.


T 4/2/13

HW due: Work on data collection activities for your group project (math facts, free throws). If your group has already gathered data (art backstory, apple juice, headphones), then begin working on your project writeup, which will be due Friday.

In class: Double quiz (10 + 10 pts.) on recent material.


W 4/3/13

HW due:

1. Work on projects.
2. Prepare for yet another quiz (10 pts.) over recent material.


Th 4/4/13

HW due:

1. Work on projects.
2. Prepare for yet another quiz (10 pts.) over recent material.


F 4/5/13

HW due:

Project writeup (100 pts. per student) should be submitted by 3:00 p.m. unless your group has obtained written permission for an extension. Project write-ups should be approximately 2-5 pages long and should include subheadings similar to these:

Research question
Background description (optional)
Lessons learned/directions for possible future research
Appendix A: Raw data (1 row per test subject, 1 column for each fact gathered from that subject). Identify each subject by name or, if anonymity is important, by subject number.
Appendix B: Group leader report

For example, in a project designed to see whether light level affects performance on an IQ test, your raw data table might look something like this:

Important: The group leader is responsible for submitting a paragraph stating what each person did (concrete tasks, not generalities) and recommending a point split. The recommendation of the group leader is usually respected unless there are extenuating circumstances. The group leader report is worth 10 points for the group leader only.

Example of an acceptable group leader report:

I recommend an equal point split (max. of 100 points per student), since the workload was shared approximately equally. I organized the project, submitted all of the original methodology homework assignments after phoning Sam and Ted, was present at the data collection, and double-checked the P-value and conclusion. Sam designed the double-blinding procedure and recommended a methodology enhancement that saved us a great deal of time. He also caught a mistake that, if he had missed it, would have reversed our conclusion. Finally, Ted was the workhorse of the data collection, implementing all of the procedures exactly according to plan, and he also wrote the initial draft of the full report. After Sam and I reviewed the draft and made changes, Ted also was the final proofreader.

Example of an unacceptable group leader report:

I recommend splitting the maximum possible 300 points with 90 to me, 105 to Sam, and 105 to Ted. They both did a little more work than I did. I slacked off in the beginning, and they had to carry me for awhile. They are both really great guys, I think you would have to admit.


M 4/8/13

HW due: Work on AP review questions from your review book. Work a minimum of 1 free-response question and 5 multiple-choice questions. More are certainly encouraged. Keep a written record of the problems you worked on.


T 4/9/13

HW due:

1. Continue working on AP review questions from your review book. This time, work at least 10 multiple-choice questions. For each one, write the page number, the question number, the scratch work (if any—legibility is not required), the answer you committed to, the correct answer, and the learning that took place as a result.

On the real exam, you are required to work 40 questions in 90 minutes, which gives you an average of 2 minutes and 15 seconds per question.

2. Glance at the Must-Pass Quiz and start thinking about it. Everyone is required to pass this quiz before the end of the semester.


W 4/10/13

HW due:

1. Work problem #5 from last year’s AP exam. Allow about 13 minutes to write your answers. Write legibly!

2. Use the scoring guidelines for question #5 to assign a score of E, P, or I (essentially correct, partially correct, or incorrect) for each part. In other words, you need a score of E/P/I for part (a), another score of E/P/I for part (b), and another score of E/P/I for part (c). Carefully follow the instructions in the scoring guidelines when assigning your scores.

3. Using the instructions on p. 16 of the scoring guidelines, compile your score into a numeric score of 0, 1, 2, 3, or 4. Circle your answer! Note that the scoring guidelines translate as follows, where scores are arranged in decreasing order:

     EEE = 4
     EEP = 3
     EEI, EPP, EPI, or PPP = 2
     EII or PPI = 1
     PII or III = 0

4. Prepare for the Must-Pass Quiz. One or more randomly chosen students will take the quiz today, for real.


Th 4/11/13

HW due:

1. Work problem #6 from last year’s AP exam. Allow about 25 minutes to write your answers. Write legibly!

2. Use the scoring guidelines for question #6 to assign a score of E, P, or I (essentially correct, partially correct, or incorrect) for each part. In other words, you need a score of E/P/I for part (a), another for (b), another for (c), and another for (d).

3. Using the instructions on p. 20 of the scoring guidelines, compile your score into a numeric score of 0, 0.5, 1, 1.5, 2, 2.5, 3, 3.5, or 4. Circle your answer! Note that the scoring guidelines translate as follows, where scores are arranged in decreasing order:

     EEEE = 4
     EEEP = 3.5
     EEEI or EEPP = 3
     EEPI or EPPP = 2.5
     EEII or EPPI or PPPP = 2
     EPII or PPPI = 1.5
     EIIII or PPII = 1
     PIII = 0.5
     IIII = 0

4. If your score is not an integer, you must be prepared, in class, to state why your score should be rounded up or down. The final AP scoring is always an integer.

5. Continue preparing for the Must-Pass Quiz.


F 4/12/13

HW due:

1. Choose either A or B below. Assignment B is available as an option only for students who are taking the AP exam.

    (A) Use your random number generator to choose an SRS of 15 multiple-choice questions from Practice Exam I in the Barron’s review book. Set a time limit of 34 minutes. (Use an oven timer or a clock that has a second hand.) Record your answers on your HW paper, including scratch work, if any. Then, check your answers against the key. For any questions that you missed, mark the correction in a different color (e.g., red) and write a phrase or a short sentence summarizing what you learned.

or  (B) Do part (A), except with a smaller SRS of 7 questions and a time limit of 16 minutes, Then, write a thoughtful paragraph describing exactly how you will prepare for the AP exam between now and May 10. Note: The wording of this assignment is intentional. You are not to describe what you intend to do or hope to do; you are to describe what you will do. You are making a commitment to yourself. Be realistic, and be truthful. Legibility is required.

2. Continue preparing for the Must-Pass Quiz.


M 4/15/13

HW due:

1. Write #4 from the 2011 Form B exam. Set a timer for 13 minutes. Then use the scoring guidelines to develop a score for yourself, as you did last week. The scoring guidelines are on pp. 11-13 of this file.

2. Prepare a list of at least 5 review questions. These can be questions of your own, or they can be questions you found elsewhere. Then circle the one question you think is “best” for today’s in-class review. (Obviously, this is subjective, and what you think is best for you may or may not be best for the class as a whole.) The three (3) students whose selected questions are judged “best” by Mr. Hansen will earn immunity from one question on tomorrow’s test.

In class: Review.


T 4/16/13

Test (100 pts.) on everything (all topics for the entire year). Emphasis on hypothesis testing, especially these areas:


·          g.o.f.

·          2-way

·         LSRL t-test


W 4/17/13

No class (Alumni Day).


Th 4/18/13

HW due: Select any 12 multiple-choice questions from your review book. Spend the first few minutes recording the page number and problem number for each question. (Enter this table on your HW paper. Leave some blank space to use for scratch work) Then set a timer for 27 minutes, which is AP pace. With your remaining minutes of homework time, look up the correct answers and mark corrections in a different color.

Hint: Try to select questions that are hard enough for you to miss some, so that you can learn something, but not so hard that you ignore them and guess on many of the answers. Getting 8 or 9 correct out of 12 is a good score for review practice.


F 4/19/13

HW: Same as yesterday (12 more multiple-choice questions, 27-minute timer, plus corrections).


M 4/22/13

No school (Phi Beta Kappa Day).


T 4/23/13

HW due: Choose any 2 free-response questions that you wish, either from your AP review book or from this site. Record the source and problem number on your HW paper. Set a timer for 26 minutes, and grade your work when you have finished.

Note: If you intend to take the AP exam, you should really do a minimum of 4 questions. However, 2 questions will be sufficient to qualify for full HW credit.


W 4/24/13

HW due: Another 2 free-response questions, with a 26-minute time limit. Follow the same instructions as in the 4/23 calendar entry.


Th 4/25/13

HW due: A “#6” question, either from your review book or from this site. Follow the same instructions as in the 4/23 calendar entry. Time limit for the write-up is 25 minutes.


F 4/26/13

HW due: Same as for Thursday, 4/25 (i.e., another “#6” question). Set your timer for 25 minutes, and then consult the grading rubric. Write your score on your HW paper, along with anything useful you learned as a result.


M 4/29/13

HW due: AP review, freestyle. Keep a time log and a written record of your work and corrections. Suggested time is 70 minutes (2 of 3 days, minimum of 35 minutes each). Those not taking the AP exam will receive full credit for 35 minutes or more of logged problems.


T 4/30/13

HW due: Continue working your AP review problems.

In class: Quiz (30 pts.) on the AP formula sheet. You need to understand what each formula is for. Many of them are useless, but you need to know which ones!


W 5/1/13

HW due: Write another 35 minutes’ worth of AP review problems (multiple-choice or free-response, your choice). Be sure to log the page number and problem number for each one that you do. Timing is 2 minutes and 15 seconds for each MC problem, 13 minutes for each “regular” FR problem, and 25 minutes for each “project-type” FR problem. The longer FR problems are always #6 if you use a practice or actual AP exam.


Th 5/2/13

Giant Quiz (70 pts.) in AP format. There will be a mixture of MC and FR problems, using AP timings and an AP-style scoring curve.


F 5/3/13

HW due:

1. Score your work on 2007 free-response question 4, using the scoring guidelines furnished.

2. Minimum of 35 minutes’ worth of AP review problems (multiple-choice or free-response, your choice). You may count task #1 toward your total time.


M 5/6/13

HW due (optional): Continue working each day on AP review problems.


T 5/7/13

HW due: Set a timer for 25 minutes and do #6 from the 2006 Form B exam. Then, read the scoring guidelines for #6, and write corrections on a separate sheet of paper. If your score is 1 or 2, also write a metaknowledge statement describing (1) what you did know as you tackled the problem and (2) what you now realize you did not know. Your assignment will be graded based on completeness, legibility, and honesty.


W 5/8/13

HW due: Write another 35 minutes’ worth of AP review problems (multiple-choice or free-response, your choice). Be sure to log the page number and problem number for each one that you do.

In class: Wrap-up (let’s hope!) of the Must-Pass Quiz, followed by the Notation Jar contest. Notation Jar will result in a grade for Luke, Sam, and Victor, who misread the instructions on the 4/16 test, but for everyone else, it will be pure, unalloyed fun. It may even be educational, as we prepare for the AP exam.


Th 5/9/13

HW due: Write another 35 minutes’ worth of AP review problems (multiple-choice or free-response, your choice). Be sure to log the page number and problem number for each one that you do.


F 5/10/13

AP Exam, Trapier Theater. Arrive by 11:45 (right after class), since the exam will begin early.

HW due:

1. (Suggested, especially if you are taking the AP exam.) Write another 35 minutes’ worth of AP review problems (multiple-choice or free-response, your choice). Be sure to log the page number and problem number for each one that you do.

2. (Required of everyone.) Make a list of 3 or more concepts or questions that you find baffling. If there is a question you find baffling, you can record the page number and problem number to save writing. If there is nothing you personally find baffling, then make a short list of concepts or questions that you think other students might find baffling.

In class: AP review and final Q & A. Bring your most baffling questions! Please attend, since we are going straight from this class to the AP exam itself. If you prefer to spend D period studying on your own, that is OK, provided you turn in your HW at the beginning of the period.


M 5/13/13

HW due: Estimate the following probabilities. Enter your guesses in writing, and record them on a standard HW sheet. It is not expected that you have the capability to answer all of these questions accurately. An estimate is acceptable. Heein is permitted to use the same HW sheet for both HappyCal and STAtistics.

1. Player A rolls 2 fair dice. Player B rolls 4 fair dice. The probability of interest is the probability that the maximum die roll for A is strictly greater than the maximum die roll for B. For example, if A rolls (2, 5) and B rolls (3, 4, 3, 2), then max(A) = 5 > Max(B) = 4, and player A wins. However, if A rolls (5, 2) and B rolls (5, 1, 1, 4), then max(A) = 5, max(B) = 5, and B wins. We want to know the probability that player A wins.

2. A random stream of 15,000 decimal digits is spewed out by a digital device whose job it is to spew out random digits. The digits follow an approximately uniform distribution, but of course there is no guarantee that the number of 0’s, 1’s, 2’s, etc. are exactly 1500 each. The probability of interest is the probability that the sequence 2, 0, 1, 3 appears exactly twice when the digits are viewed in order. The two occurrences of 2 0 1 3 may have any number of intervening digits (0 or more) between them, but each occurrence of 2 0 1 3 must have those digits as consecutive digits.

3. Ten quadrillion (i.e., 1016) random capital letters, A through Z, are generated. What is the probability that the word SHAKESPEARE appears at least once in that immense list when the letters are viewed in order?

4. Two cards are drawn without replacement from a standard, well-shuffled 52-card deck. Given that at least one of the cards is an ace, what is the probability that you have a pair of aces?

5. Two cards are drawn without replacement from a standard, well-shuffled 52-card deck. Given that the first card is an ace, what is the probability that you have a pair of aces?


T 5/14/13

No additional written HW is due today.


W 5/15/13

HW due:

Note: For all questions, both Monday and today, an estimate within  percentage point of the true value is desired. For example, if the true answer is 0.941, you would not be considered correct if you said “1,” even though that’s not a terrible guess. After all, in real life, there’s a large difference between something that is true 94.1% of the time (think of correct order execution at your favorite fast-food restaurant) and something that is true 99.999% of the time (correct air-traffic control for an arriving flight).
1. Estimate the probability of drawing a jack as the next card from a well-shuffled deck, given that the leftmost card of the 2 cards you already hold is an ace. The rightmost card of the 2 you already hold is not visible to you.

2. Estimate the probability of drawing a jack as the next card from a well-shuffled deck, given that at least one of the 2 cards you already hold is an ace. (You do not look at either of the cards you are already holding. Assume that you have already asked a trusted friend, “Is at least one of these cards an ace?” and that she said yes.)

3. Explain how knowledge of the calculus helps in answering Monday’s question #3. Hint: If you haven’t studied the calculus, a vague explanation will suffice.

4, 5. What two important metaknowledge life lessons have you learned as a result of Monday’s and today’s HW? If you learned a third lesson (or more), feel free to write more.

6. Read the “Excelcise” (10/28/010 calendar entry at this link), and become somewhat familiar with the steps. We will practice doing this in class, and you will eventually be required to perform all the steps in under 5 minutes. The record time is slightly under 2 minutes.


Th 5/16/13

Friday schedule is in effect today.

HW due: Practice your skills on the Excelcise (see 10/28/010 calendar entry). In class, you will be expected to produce the final spreadsheet within 5 minutes without using any macros or copied-and-pasted text from external files. Copying and pasting within your spreadsheet (e.g., Edit, Paste Special, Transpose) is permitted.


F 5/17/13

Thursday schedule is in effect today.

HW due:

1. Practice your skills on the Excelcise (see 10/28/010 calendar entry). In class, there will be no practice time; we will cut straight to the 5-minute competition.

2. Determine, using any means available to you, the probability of selecting at least one ace in 8 draws (without replacement) from a well-shuffled standard deck of cards. Show your work, and give your answer with m.o.e. and confidence level.


M 5/20/13

15th Annual Field Trip to the National Cryptologic Museum, Fort Meade, MD. Bus departs at 8 a.m. from near the intersection of Garfield St. and the service road near Grant Meadow. We will return at approximately 1 p.m. after a guided tour of the museum and an interactive lecture by a working NSA mathematician. Regular school dress code is required.

If you prefer not to go on the field trip for some reason, be sure to say so. In that case, you are expected to attend all your other classes, A through F periods.


T 5/21/13

7:25 a.m.: It’s JBAM a at McDonald’s Week!

In class: Guest speaker on cybersecurity, Mr. Joe Morris ’62.


W 5/22/13

7:25 a.m.: It’s JBAM b at McDonald’s Week!

In class: Guest speaker on Big Data, Mr. Fred Richards. If you have not already passed the Excelcise, you will need to come in after school to get that credit recorded.


Th 5/23/13

HW due: Excelcise (Sam, Trevor, Frank, and James only).


F 5/24/13

Last day of classes.



Essential Links:
STA School Handbook
-- College Board: AP Statistics Course Description
-- College Board: more than 100 AP free-response questions and scoring rubrics from previous years
-- Our old textbook’s site has online quizzes and some useful links
-- RVLS (Rice Virtual Lab in Statistics): One of the best sites anywhere for statistics! Here you’ll find a complete college statistics course (complete with clickable glossary and great case studies), simulations, and some excellent analysis tools.
-- Virtual Laboratories in Probability and Statistics (University of Alabama at Huntsville)
-- StatCrunch 3.0 (formerly WebStat): An on-line statistical computing package (requires Java)
-- How to study statistics (written by a professor at the University of Central Florida, but the ideas are valid for our class)
-- Eric Weisstein’s World of Mathematics: a monstrously huge hyperlinked reference
-- The Must-Pass Quiz for Statistics: doubles as a review for the AP exam

TI-83 Links:
CINT (converts confidence interval from interval notation to the more convenient “estimate ± m.o.e.” format)
-- INVT (inverse t) program written by Mr. Hansen and the Class of 1999
-- CHISQGOF (Chi-Square Goodness of Fit) program also written by Mr. Hansen and the Class of 1999
-- CSDELUXE (Chi-Square Deluxe): combines CHISQGOF and STAT TESTS C into one package; written by Mr. Hansen for the Class of 2003
-- Modifications to SCATRBOX program so that it returns the LSRL equation at the end (follow-on to a stat teacher workshop I attended on 12/5/2001)
-- David Pachner’s statistical test and confidence interval files for the TI-83 (added 4/16/2001; not reviewed by Mr. Hansen for accuracy)
-- TI-83 programs from Texas Instruments

Philosophical Links:
-- In praise of Bayes: a very readable overview of the tension between the standard (“frequentist”) approach to probability and the Bayesian view

Controversial Links:
-- Does an elite college really pay? Article addresses the issue of whether you would do better financially if you simply invested the difference in tuition price.
-- Does traditional hypothesis testing actually make sense? Article questions whether the entire second semester of our course is a waste of time . . .
-- Are law schools cooking their ranking statistics? Every high school statistics student should read this (and maybe a second time, four years later).

Fun Links:
-- Guessing correlation coefficients by eye
-- Another correlation game
-- Photos from our 5/20/99 field trip to the National Cryptologic Museum at the NSA
-- Huge Internet gallery of statistics jokes (warning: many are excellent, but some are dangerously lame)
-- Average age at death for rock stars is 36.9 (vs. 75.8 for the overall population). . . this site is religiously oriented (and apparently sincere), but the reasoning process is seriously flawed. Can you find the problem?
-- Chance Database Welcome Page (this is the link cited in the 4/4/99 Washington Post Unconventional Wiz column)
-- Accident statistics (the taxicab problem)
-- Psychological probability quiz
-- Marilyn is Wrong! (a truly great site, even though it doesn’t seem to include Dr. Morse’s response to Marilyn yet)
-- Male sweat may be good for women’s health (a scholarly article with p- and t-values from 2003, plus an abstract in 2007)
-- Lying with statistics
-- One of the biggest marketing blunders of all time: the New Coke fiasco
-- More fun links on Mr. Hansen’s home page

Serious Links (click here)

Extra Credit (please see me if interested):
-- American Statistical Association poster or project competition, deadline 4/1/2012 if you desire extra credit
-- Washington Statistical Society Curtis Jacobs Memorial Prize, deadline 5/4/2012
-- Other extra credit options are available under the Fun Links at modd.net (see Mathcross Puzzles)

Group Projects (1998 onward):
Exploratory Data Analysis
-- Assignment (2005-06)
-- Results (1998-99)
-- Results (1999-2000)
-- Results (2000-01)
-- Results (2005-06)
Opinion Survey
-- Assignment (2000-01)
-- Results (1999-2000)
-- Results (2000-01)
Experimental Design and Execution
-- Assignment (2000-01)
-- Results (1998-99)
-- Results (2000-01)
Pairs Project on How to Lie With Statistics and P-value Calculations
-- Assignment (2000-01)
-- List of Partners (2000-01)
Critique of a Scientific Article
-- Assignment
AP Review
-- D period (1998-99)
-- F period (1998-99)

Test #1 (Chapters 1-2 plus §3.1 of old textbook), Sept. 2000:
-- Test #1

Old Test #1 (Introduction through Section 2.2 of old old textbook):
Study guide
-- Test #1D--has a residual plot question not found in the F period version
-- Test #1F

Test #2, Oct. 1998:
-- Mr. Hansen’s study guide
-- Eric Love’s study guide (1/12/1999 revised version)
-- Test #2 (merged version, with comments)

Test #3 (Chapter 5) for 1999-2000
-- Answers to practice test (the practice test was handed out in hard copy form on 11/15/1999)
-- Take-home portion distributed 11/16/1999, due 11/17/1999

Old Test #3 (Chapter 4 of old old textbook):
-- Study guide
-- Test #3 (merged version)
-- Answer key

Test #4 (Sections 5.1, 5.2, 6.1 of old old textbook):
-- Study guide
-- Test #4D
-- Test #4F

Test #4 (Chapters 7 and 8 of old textbook: random variables, binomial & geometric distributions):
-- Actual test, 1/29/2004

Test #5 (Sections 6.2, 6.3, 7.1 of old old textbook):
-- Study guide
-- Practice test
-- Answer key for practice test (incl. correction to #18 suggested by C. Muller)
-- Test #5 (merged version)

Test #5 (Sections 7.2 through 9.1 of old textbook):
-- Actual test, 2/6/2002

Test #6 (Sections 7.1-7.3 of old old textbook):
-- Practice test
-- Answer key for practice test
-- Test #6D, with answer key

Test #6 (Chapters 9 and 10 of old textbook):
-- Actual test, 3/7/2002

Test #7 (Sections 8.1-8.3 of old old textbook, plus Chi-Square GOF):
-- Answer key for sample test problems
-- In-class portion
-- Take-home portion

Test #8 (Section 9.1 of old old textbook, plus Geometric Probability Distributions):
-- Take-home test due Wednesday 4/28/1999
-- Answer key (not yet released)

AP Exam Review
-- Real sample AP questions from the College Board
-- TI-83 Function Summary
-- TI-83 STAT TESTS Summary, including the assumptions you need to check
-- PHA(S)TPC procedures, a systematic way of performing statistical tests and calculating confidence intervals
-- LSRL Top Ten
-- Normal vs. Binomial: What are the hallmarks and differences? (Includes many example problems, with solutions.)
-- Formula sheet markup guide
-- Guide to standard error formulas (third page of the AP formula sheet)

Question of the day: 12/15/1998

Preview of quiz for Wednesday, 11/18/1998

Return to Mr. Hansen’s home page

Return to Mathematics Department home page

Return to St. Albans home page

Last updated: 22 May 2013