2.5STATISTICS IN SUMMARY
Chapter Specifics
• We select a sample in order to get information about some population.
• How can we choose a sample that fairly represents the population? Convenience samples and voluntary response samples are common but do not produce trustworthy data. These sampling methods are usually biased. That is, they systematically favor some parts of the population over others in choosing the sample.
• The deliberate use of chance in producing data is one of the big ideas of statistics. Random samples use chance to choose a sample, thus avoiding bias due to personal choice.
• The basic type of random sample is the simple random sample, which gives all samples of the same size the same chance to be the sample we actually choose.
• To choose an SRS by hand, use a table of random digits such as Table A in the back of the book, or use software.
The first step in reasoning from data to a conclusion is obtaining data. In Chapter 1, we discussed sample surveys as one way to collect data in an observational study. The method of selecting the sample in a sample survey affects how well the sample represents the population. Biased sampling methods, such as convenience sampling and voluntary response samples, produce data that can be misleading, resulting in incorrect conclusions. Simple random sampling avoids bias and produces data that give us confidence that the first step in our argument is sound.
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In the next chapter, we look more closely at what a simple random sample tells us about the population from which it is selected. And in Chapter 4, we discuss some of the problems faced by people who take surveys in the real world.
CASE STUDY EVALUATED To participate in the MLive poll described in the Case Study that opened the chapter, you had to choose to go online to the MLive website and click on one of the possible responses. Use what you have learned in this chapter to assess whether the data collected in such an online poll are good or bad. Your assessment should be written so that someone who knows no statistics will understand your reasoning.
Online Resources
•The Snapshots video Sampling discusses the importance of sampling, the basics of sampling, simple random sampling, and some practical issues in selecting random samples.
•The video technology manuals explain how to select an SRS using Excel, JMP, Minitab, and the TI 83/84.
•The Statistical Applet Simple Random Sample can be used to select a simple random sample when the number of labels is 144 or fewer.