312 CHAPTER 7 Estimating Parameters and Determining Sample Sizes 7-3 Estimating a Population Standard Deviation or Variance • Develop the ability to construct a confidence interval estimate of a population standard deviation or variance, and be able to interpret such confidence interval estimates. 7-4 Bootstrapping: Using Technology for Estimates • Develop the ability to use technology with the bootstrapping method to construct a confidence interval estimate of a population proportion, population mean, and population standard deviation and population variance. Key Concept This section presents methods for using a sample proportion to make an inference about the value of the corresponding population proportion. This section focuses on the population proportion p, but we can also work with probabilities or percentages. When working with percentages, we will perform calculations with the equivalent proportion value. Here are the three main concepts included in this section: ■ Point Estimate: The sample proportion (denoted by p n) is the best point estimate (or single value estimate) of the population proportion p. ■ Confidence Interval: We can use a sample proportion p n to construct a confidence interval estimate of the true value of a population proportion p, and we should know how to construct and interpret such confidence intervals. ■ Sample Size: We should know how to find the sample size necessary to estimate a population proportion p. The concepts presented in this section are used in the following sections and chapters, so it is important to understand this section quite well. Below are the key notations that will be referenced. Notation: x = number of successes n = sample size N = population size pn = x>n denotes the sample proportion p = x>N denotes the population proportion PART 1 Point Estimate, Confidence Interval, and Sample Size Point Estimate If we want to estimate a population proportion with a single value, the best estimate is the sample proportion pn. Because pn consists of a single value that is equivalent to a point on a line, it is called a point estimate. 7-1 Estimating a Population Proportion DEFINITION A point estimate is a single value used to estimate a population parameter.
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