STATISTICS IN SUMMARY

Chapter Specifics

image This chapter continues the discussion of probability that we began in Chapter 17. Here, we examine the formal mathematics of probability, embodied in probability models and probability rules. Probability models and rules provide the tools for describing and predicting the long-run behavior of random phenomena.

In this chapter, we also begin to formalize the process, first mentioned in Chapter 3, of using a statistic to estimate an unknown parameter. In particular, the sampling distribution will be the “probabilistic” tool we use to generalize from data produced by random samples and randomized comparative experiments to some wider population. Exactly how we do this will be the subject of Part IV.

CASE STUDY EVALUATED Look again at Table 18.1, discussed in the Case Study that opened the chapter.

  1. 1. Do the probabilities in this table follow the rules given on page 429?

  2. 2. On some websites, the probabilities are given as betting odds of winning. If you are a bookie setting betting odds, should you set the odds so the probabilities sum to greater than 1, exactly 1, or less than 1? Discuss.

image Online Resources

  • The Snapshots video Probability introduces the concepts of randomness, probability, and probability models in the context of some examples.

  • The StatBoards video The Four Basic Probability Rules discusses the basic probability rules in the context of some simple examples.