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Homework Notes Chapter 6

Chapter 6: [6.1, 6.3, 6.5, 6.7, 6.8 – 6.17], 6.19, 6.20, 6.21, 6.22, 6.23, 6.25, 6.27, 6.31, 6.32

It is NOT a good idea to use software in this chapter. The computations here are finding percentages. The important work is figuring out what numbers to divide. If you use software, it will compute percentages, but it will not always be clear to you how to tell it to compute the percentages that are actually needed. Most students find it more confusing to use software here than to do the problems by hand with a calculator.

6.1, 6.3: We might think that it is a hassle to use the technical terms of “marginal distribution” and “conditional distribution.” I have found, however, that it is usually easier for students to answer these questions correctly than some of the later questions. These are useful concepts for you.

6.5. Many answers are possible. But you do have to find numbers that meet all the conditions for the totals.

6.5. While the solution in StatsPortal is quite complete, I find that students often have trouble deciding which distributions to compute to answer questions like this. This is an illustration of the discussion in the second half of the last paragraph before these exercises. Here the response variable is whether the person has arthritis later in life. That’s the response variable because the exercise says that this is a study of arthritis and we are investigating whether the types of experiences playing soccer affect whether the arthritis occurs. So, we need the conditional distribution of arthritis or not for each of the three types of soccer players.

6.7. Problems like these can be confusing. This is very similar to the example. Use that idea. Think about it carefully so that you are prepared to do other problems of this type that are not quite so similar.

6.19-6.23. It is very important to be able to take a question which asks for a percent and figure out what number should go in the denominator. Often it is what follows “of” in the statement. Use these problems to refine your ideas of how to decide what fraction to write to find the requested percentage each time. Do you find the problems asking for the marginal distribution and the conditional distribution easier or harder than the others. Discuss this with other students.

6.25. Data given in this manner is sometimes called a three-way table. That’s because it shows the relationships between three variables – gender, whether they were admitted, and which type of school.

a. The hardest thing for students to understand about this question is that the two-way table, which is your answer, DOES NOT contain all the information shown in the three-way table. You lose the information about what school it is, because you sum up, so you can’t see how many are from each school in the resulting two-way table.

To make a two-way table from a three-way table, I think the first thing to do is to label the categories. (When you get them labeled then read the labels to see what numbers are needed in that cell.) Since the question says “two-way table of gender versus admission decision” then, on one side you have the categories of gender and the other side is the categories of admission decision.

b. Nothing to say more than what’s in StatsPortal.

c. Here, you must go back to the original three-way table to find the data to compute these percentages.

d. Remember the general idea we saw back in exercise 6.7 – look for whether two groups had different proportions of “easy” cases. What would “easy” mean here? And what are the two groups? (Answer: “Easy” means easier to get into the program. The two groups are male and female applicants.)

6.27 -6.31. These are very important problems and often confusing to students. The key idea is to determine which is the response variable in the question, and to use the guideline in the last six lines at the bottom of page 166 to analyze these. Ask if this isn’t clear.

6.32. Here you must make the table yourself and then think about what numbers to pull from it to find percentages that are relevant to this question. This is not easy. For part b, after you have computed some percentages, then explain as clearly as you can in words what they tell you about this question. If you can’t think of how to do that, it is a clue that you may have not made a good choice about what percentages to compute.

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