Information and Comments about the Final Exam

• Time: Wednesday April 18th, 4-7 p.m.
• Location: SE Gym
• Aids Allowed: Calculator and two 8.5 by 11 two-sided formula sheets. You may write anything you like on the formula sheets. Tables of the standard normal distribution and the t-distribution will be supplied.
• Coverage: The final exam is comprehensive, but there is just one question about descriptive statistics, sampling and so on. See the breakdown of points below.

Point Breakdown: The final exam has 12 questions on 12 pages, but it is not exactly one page per question. You will answer the questions on the exam paper. Here are the main topics and number of marks for each topic. There is a total of 100 marks.

• Descriptive statistics and sampling: 5 marks
• Probability and discrete distributions (Basic stuff, Venn diagrams, Conditional probability and independence, expected value): 19 marks
• Normal distribution and sampling distributions: 34 marks
• Estimation of means and proportions, (Point and interval, with and without replacement, including stratified): 18 marks
• Significance testing: 24 marks

The material on the final is mostly in the order that it appeared in the course, but not entirely. I moved some problems around trying to fit several short problems on a page, and the last problem is a challenging probability problem that is really designed to discriminate between A and A+ students. It is last because that way it will be less disruptive in case you get stuck. On the other hand, it is almost exactly like one of the homework problems.

How to prepare: When you are preparing for the final, above all be guided by the homework assignments. They tell you exactly what pages in the text to read and explicitly list the concepts for which you are responsible. The assigned problems are examples of what you should be able to do.

You are also responsible for everything that happens in lecture, provided there's a homework problem on it. You can tell what problems I've made up, because they are not from the text.

There will be no problems on regression..

The final will be much like the midterm. The problems will be like the homework problems. I made it up and I will mark it.

To prepare for the final, I suggest that you

1. Go over the assigned reading in the text, treating each example from the text as a problem with full solution. Try to solve it yourself, and then look at the answer only when you are done, or if you are really stuck.
2. Do the same thing with all the examples from lecture.
3. Re-do most of the homework problems. However, see the comment immediately below.

Some of the homework problems have no content; they are designed to provide practice in doing the right calculations, without the distractions of a word problem. What I mean is something like this. We select a random sample with n=9 from a normal distribution with μ=50 and σ=10. What is the probability that the sample mean will be less than 40? You will not see anything like this. All the questions on the final are word problems.

Miscellaneous comments (some based on the midterm)

• Read the questions carefully, and answer what is asked.
• Typically you will have more room than you need for an answer. In some cases I gave a huge amount of space for a short answer just because I wanted to start the next question on a new page. Do not think you have to fill up the space provided. When I made up my answer key, there was a lot of white space showing.
• Independence is not the same thing as being mutually exclusive.
• P(A|B) is not the same as P(AB). In a word problem, "and" is not the same as "given."
• Consider word problem examples from the text and lecture as case studies in translation. For example, A phrase like "Fifteen percent of the apples transported by truck were bruised" means that the probability of Bruised given Truck is 0.15. It's a conditional probability.
• P(A) is not the same as P(AB^c). Events can overlap! Make a Venn diagram with overlapping events A and B. If you cannot see what I am talking about from the picture, then this is something you need to review.
• Sometimes you are given population parameters and asked about the probability of a sample total. At other times you are given sample statistics and asked about the probability of a population total. There are two different approaches to these two different kinds of problem; be aware of which world you're in at the moment.
• If you are given population parameters (Greek letters or the letter p) you are living in the world of probability. If you are given sample values but not population parameters, you are living in the world of statistics. What if it's a word problem? Well, if you see some blanket statement like "The mean amount of water flowing through the sluice gates of a dam during a 24-hour period is 11.2 million litres," it's likely μ.
• The null hypothesis is always about population parameters. It is never about statistics. If the statement of a null hypothesis makes any mention of a sample quantity like the x-bar, it is completely wrong.
• Sometimes you may be given population parameters and asked about the probability of a sample total. At other times you may be given sample statistics and asked about the probability of a population total. There are two different approaches to these two different kinds of problem.
• During the midterm, several people asked how many decimal places I wanted. I didn't really know then, but this time I payed attention. When in doubt, keep 4 decimal places in intermediate calculations, and express the final answers to two decimal places. This applies unless the answer is a probability from the normal table, in which case the answer is to 4 decimal places. I gave guidelines on this in many problems, but not all. There's one problem where I said don't round, and there it's important, because you will be dividing by a small number, and if it's inaccurate the answer will be way off.

  You should not lose any marks for rounding error unless it's really gross, and even then the deduction should be minor. However, it's better for both of us if we do it the same way.

• Following directions from my employer, I have placed the following warning on the first page of the final exam:

  It is an academic offence for students to possess the following items at their examination desks: cell phones, pagers of any kind, IPODs, MP3 players, wristwatch computers, personal digital assistants (e.g., palm pilots) or any other device that is electronic. If any of these items are in your possession now, please ensure they are turned off and put them with your belongings at the front (or side) of the room before the examination begins - no penalty will be imposed. A penalty WILL BE imposed if any of these items are kept at your examination desk.

  Please take this seriously! Though I will be present at the exam, the University supplies a "chief presiding officer" who is technically in charge, and this person might nail you if your cell phone rings during the exam, even if you forgot it was in your pocket.

About the marking: I will mark the final exam pretty much the way I marked the midterm, though perhaps a bit more gently, to recognize that you will be tired and stressed. Some students perceived my marking of the midterm as overly harsh; they got lots of zeros, and thought I was not giving any partial credit. In fact, I gave substantial partial credit, and the percentage of As on the midterm happened to agree exactly with the university's guidelines for the maximum percentage of As in a course. The comments below may help to clarify my marking standards, and if you are aware of them, it might translate into a higher score on the final.

Looking back over these comments, I see that a common theme is that you are expected to show understanding. Carrying out some procedure is worthless unless it is guided by understanding of what you are doing and why you are doing it.

• Read the questions carefully. Answer the questions that are asked. If you give a completely correct answer to a related question (likely from the homework), you'll receive no marks. A memory dump is something to avoid, unless you are sure that the question is exactly from the homework (a few of them are).
• In some courses, students are rewarded for adopting a "shotgun" strategy, in which they write a whole bunch of stuff that is somehow related to the question. Chances are, they will say at least part of what the professor is looking for, and they will get some marks. In my courses, a shotgun answer is a big mistake. It tells me that you don't know what's going on, or the only way you can think is by free association, or that you can't even make yourself pretend that this makes a difference for the three hours you are taking the final exam. Please focus on the question, and give one answer to the question. If you give two contradictory answers and one of them is completely correct, you will likely get a zero. You are responsible for everything you write. If you have a false start or you're just writing things to help you think, fine, but scratch it out, and clearly indicate which answer you want me to look at.
• Sometimes, natural and fairly minor mistakes in calculation can lead to answers that are simply impossible. An extreme example is a negative probability, or a probability greater than one. If you find yourself in this situation, first look back and try to find the error and correct it. If you can't find the error, please don't just settle for a crazy answer. Write a comment about it, like "I know probabilities can't be negative; I must have made a mistake somewhere." In that case I will look carefully to try to find your mistake, and likely make only a small deduction if it is a mechanical error, and not conceptual. On the other hand, if you leave a crazy answer with no comment, I will give the entire question a zero, or at least deduct most of the marks.

  When I have given advice like this in the past, some students have included a phrase like "I know this must be wrong, but ..." in almost every question. Please don't do this either!

• If you have a formula sheet and you write down the correct formula, and then you do nothing correct with it, it gets a zero. This is the down side of having a formula sheet, but the advantages of having a formula sheet clearly outweigh the disadvantages. Don't expect marks for demonstrating a vague familiarity with the topic. In this course, as in real life, it is worth nothing.