Test Reviews

(See caution at the end of the document.)

Test Reviews:

These Test Reviews are not intended to replace doing the classwork and doing the homework These are not lists of objectives for the chapters nor are they complete lists of the topics. The textbook and homework provide those. These Test Reviews focus on topics and problems that students in previous semesters have been somewhat more likely to make mistakes on than the rest of the material.

It is pointless to even read these questions until you have read the chapters and done the homework. After that, you might want to write out answers to the questions (maybe conferring with other students in your class) and then bring the questions and your answers to the instructor or a tutor so that they can help you with any misunderstandings you have.

Test 3:

Be sure that you understand all the material from the first two tests, particularly any problem on those tests that you lost points on. On Test 3, you may have questions on anything in the course so far. In particular, be sure to review all the material about sampling and experimental design.

Read the chapter summaries at the ends of the chapters and also in the review chapter and use them and your homework as guidelines for what to put on your page of notes. Then look over the following comments about things that students sometimes miss on tests to make sure you understand these.

1. What are the basic rules of probability? (sum to 1, all are non-negative.)
2. Be able to compute probabilities for discrete distributions, with only a few values, and for various continuous distributions, like normal distributions and uniform distributions.
3. How do you approximate the sampling distribution of a statistic? (Chapter 11, number 43)
4. Be able to discuss what assumptions about the dist'n of the population are needed to justify using the normal dist'n as the sampling distribution of the statistic X-bar. (See the pictures of distributions for the Central Limit Theorem.)
5. Be able to draw and correctly label the two pictures (of the dist'n of the population and of the dist'n of the sample mean) that are needed to analyze problems using the Central Limit Theorem. (See my examples of how to do problems using the Central Limit Theorem.)
6. Interpret a confidence interval, making clear that it is a confidence interval for the population mean, not the sample mean.
7. Form a confidence interval with any level of confidence, like 83%. Notice that you can't do that with Table C. You must use the normal table.
8. Be able to do all the steps needed to carry out a hypothesis testing problem:
   Write hypotheses.
   Define the parameter.
   Sketch and label the distribution of the statistic, given that the null hypothesis is true.
   Put your data on the sketch and shade in the p-value.
   Since your statistic here has a normal distribution, find the z-score.
   Use the z-score to find the p-value.
   Use the p-value to form a conclusion.
   Write the conclusion in a sentence that tells you something about the claim.
9. What values of the p-value make you reject the null hypothesis?
10. How do you use the "significance level"?
11. How do you complete a hypothesis testing problem if you aren't given the particular significance level? (Answer: Choose a significance level, state what it is, and make an appropriate conclusion based on that significance level.)
12. Define the p-value in words (p. 368) and relate the meaning of those words to the pictures you drew to illustrate the p-value. Be sure to include something about the alternative hypothesis in your words.
13. Recall that the hypotheses must have the parameter in them, not the statistic. When you define the parameter, make it clear that it comes from the population, not the sample.
14. How large a sample size is needed in order for you to justify using the normal distribution to do a confidence interval or hypothesis test for the problems about the population mean when the population standard deviation is known? (Answer: See the figures illustrating the Central Limit Theorem handout.)
15. All of the formulas in chapters 14-15 are based on the assumption that the data came from what type of sampling?
16. Be able to use the ideas in Chapters 8 and 9 to comment upon whether the data is appropriate to use for statistical inference.
17. Problems 15.19, 15.36, 15.37, 15.38, and 15.39 are good summary problems on Chapter 15 for the purpose of preparing for Test 3.

The following ideas are important, but will not be covered on Test 3. These ideas will be covered on Tests 4 and 5.

18. Is statistical significance the same as practical significance? If not, why are we interested in statistical significance?
19. How can we use a confidence interval to do a two-sided hypothesis test? (See page 379-380 or problem 15.25.)
20. You will not have to use the method of critical values to do a hypothesis test on a mean (page 377 and 378). It gives exactly the same results as the p-value method. For tests of some other parameters in other chapters, we may use this idea.
21. In problem 16.7, consider the p-values. What do these mean about the impact of sample size on the results of a hypothesis test? Even though this is a one-sided test, some students find it useful to compute a confidence interval for the mean in each of the three parts of problem 16.7 and notice how different those confidence intervals are. It is often easier to understand the effect of sample size on confidence intervals than on hypothesis tests.
22. Regarding the effect of sample size in problem 16.7-- some students say "This shows you can use statistics to prove anything." I say "This shows you can use statistics to prove anything that is really true." What do the students mean and what do I mean?
23. How must you be careful about the meaning of the results when you do multiple analyses? The "caution" about this is somewhat analogous to the idea about the meaning of confidence intervals that is pictured on page 347. Do you understand that analogy?
24. Given a set of hypotheses, be able to describe the Type I and Type II error. People choose a significance level by analyzing the consequences of each of the types of error.
25. We omitted the optional part of chapter 16 about computing the power of a hypothesis test. That's very interesting information. Read it if you want, and ask me questions about it. I haven't decided yet whether we'll go back and pick this up during the week at the end of the semester that we have to do optional material. If we do, it will be covered on Test 5. If we don't, it won't be covered on any test, of course.

Discussion in class always supersedes any information on the Web about what is covered on what test. I make no guarantee that the Web version will be updated as things change, although I do attempt to do so. However, it is very unlikely that very much will change at any one time, so it is completely reasonable to do much of your studying from this even if you are not sure what was said in class. If you missed any class, you should get someone's notes and read through them before you consider that you have fully prepared for the test.

This was last updated on October 23, 2006 . Mary Parker.