MATH 1342 Test 4 Review

Test Reviews:

These Test Reviews are not intended to replace doing the classwork and 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.

Proportions (use normal dist'n)		Means
One proportion	Two proportions	One mean (Pop'n std dev known -- use normal dis'tn. Pop'n std dev estimated from sample st dev -- use t dist'n.)	Two means Paired samples Independent samples (If pop'n std devs were know, we'd use normal dist'n, but in this course, they never are on these problems. So always use t dist'n.)

Test 4:

Notice that everything on Test 3 is still very relevant to Test 4. So, the first part of the Test 4 review is to go back to the Test 3 Review and make sure you know how to do everything listed on it, including the last few questions, that weren't covered on Test 3. Rework those problems from Chapters 14 and 15, if you need to do so. Be sure that your notes address how to do problems on Test 3 as well as the new material.

There are two Review sections that are relevant here:

• Read the summaries from Chapter 17, omitting those marked as Optional, which we omitted.
• Read the summaries from Chapter 22.

Main challenge: For each problem, determine which one of the five types it is. (Be sure your notes address all types.) Students do much better on Tests 4 and 5 if they deal with the review problems carefully before taking Test 4.

Secondary challenge: Communicate in full, clear, and correct statistical language. Many students think that simply getting correct numbers will earn them enough credit to do well enough on the test and so they don't pay attention to the material in the examples and quizzes about communication. Those students often get D's on the test.

• For each hypothesis testing problem, write correct hypotheses and define all the parameters correctly. (Writing the hypotheses in words alone doesn't meet either of these requirements.)
• For each type of problem, state all the necessary assumptions very precisely and determine whether the given situation meets the assumptions. If additional information is needed beyond the information given, describe what additional information is needed.
• Interpret each hypothesis test correctly, according to the instructions given in class. Give the P-value as accurately as possible from the tables provided, a significance level, and give the conclusion in terms of the question in the problem (not only "reject Ho" but "the data provide significant evidence, at the __% level, that ....(something about the question in the problem.)" or the equivalent statements if it is not correct to reject Ho.)
• Interpret each confidence interval correctly, according to the instructions given in class. Include the name of the parameter and make clear it is from the population, not the sample. Notice that understanding the actual meaning of confidence intervals for differences is somewhat more challenging than understanding confidence intervals for just one parameter.

More detailed comments:

1. If it is a question about means, determine whether you should use the normal distribution or the t distribution.
2. For each problem, be able to answer "What assumptions are necessary about the distribution of the population in order to use the method you used?" and "What assumptions about the sampling method are necessary in order to use the method you used?"
3. How can you tell whether you are being asked to find the sample size to estimate a population proportion p or a population mean, mu? What different formulas do you use in these cases? What different information do you need?
4. When you're setting up a hypothesis test problem about a population proportion p, do you know how to define p, how to find p-hat, and p-sub-0? What are each of these symbols used for? (Population proportion, sample proportion, and "claimed" proportion.) You need to be careful to use the correct symbols in your hypotheses and formulas, and define the population proportion(s) in words.
5. In the assumptions for inference on proportions, if you say "the sample size(s) is adequate so that the test statistic has a normal distribution" that is not precise enough. You must give details about how large the sample must be for whichever procedure is relevant: a large-sample confidence interval or the plus-four method of producing a confidence interval, or a hypothesis test.
6. The material in chapters 8 and 9, on producing data, is very important. Read the material in chapters 18-21 (not just skim over it and find the formulas) for more discussion of the issues about producing data. One of our goals for you in the statistics course is to increase your ability to read and understand statistical analyses. Reading chapters 18-21 (omitting the starred sections and subsections) is an excellent way to do this.
7. Data for a question about one mean or proportion must be obtained from a SRS, or it must be reasonable to treat them as if they were a SRS from the population of interest. (p. 388 -389)
8. Data for a question about two means or proportions must be obtained from SRSs or responses to two treatments (or a treatment and a control) in a randomized comparative experiment in which the subjects were randomly assigned to the treatments.
9. For means, be able to discuss the difference between the design that leads to a paired comparison and the design that leads to two-sample comparisons. For two means or two proportions, note that it is acceptable to take one random sample and then divide it into two groups, thinking of each of these groups as a sample from that population, based on the data. Problems 21.17 and 21.24 are examples of this.

The following ideas were discussed in Chapters 14-16, but not all tested on there. These ideas will be covered on Tests 4 and 5.

10. Be able to clearly define the parameters used.
11. Is statistical significance the same as practical significance? If not, why are we interested in statistical significance?
12. How can we use a confidence interval to do a two-sided hypothesis test? (See page 379-380 or problem 15.25.)
13. 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.
14. 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.
15. 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?
16. 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?
17. 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.
18. 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.

This was last updated on April 9, 2007 . Mary Parker, mparker@austincc.edu