As we mentioned in Chapter 11, probability is the tool we will use to generalize from data produced by random samples and randomized comparative experiments to some wider population. In this chapter we begin to formalize this process. We use a statistic to estimate an unknown parameter. We use the sampling distribution to summarize the behavior of a statistic in all possible random samples of the same size from a population.
More specifically, in this chapter we begin to think about how a sample proportion, , can provide information about a population proportion, p. When the sample proportion is computed from an SRS drawn from a large population, its sampling distribution has properties that help us understand how the sample proportion can be used to draw conclusions about a population proportion. The law of large numbers tells us that a sample proportion computed from a random sample from some population gets closer and closer to the population proportion as the sample size increases. The approximate Normality of the sampling distribution of the sample proportion for “large” SRSs allows us to make probability statements about possible values of the sample proportion. In the next two chapters, we will develop specific methods for drawing conclusions about a population proportion based on a sample proportion computed from an SRS. These methods will use the tools developed in this chapter.