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Unformatted text preview: Chapter 7 Inference for Distributions Chapter 7 1 Introduction • Our study of Exploratory Data Analysis proceeded in two steps: • Graphical techniques and numerical summaries for the distribution of a single variable (Chapter 1) • Graphical techniques and numerical summaries for the relationship between two variables (Chapter 2) • Our study of Statistical Inference will proceed in a similar fashion. • Inference for parameters of a single distribution. • Inference for parameters describing the relationship between two variables. • Inference for the comparison of parameters for two or more distributions. Chapter 7 2 Inference in Practice • In Chapter 6, we introduced confidence intervals and tests of significance. • Our procedures used the one-sample z-statistic. • We made the somewhat unrealistic assumption that σ was known. • Chapter 7 emphasizes some of the most common tools for statistical inference. Chapter 7 3 Section 7.1 Inference for the Mean of a Population Section 7.1 4 Introduction • Confidence intervals for the population mean μ are centered on the sample mean ¯ x . • Test statistics for significance tests also use ¯ x . • The sampling distribution of ¯ x is known when the population standard deviation σ is known. • In practice, we must also estimate σ , even though we are primarily interested in μ . • We can estimate σ using the sample standard deviation s . Section 7.1 5 Sampling Distribution of ¯ x • Suppose we have a simple random sample (SRS) from a population that has a Normal distribution with mean μ and standard deviation σ . • The sample mean ¯ x has distribution N μ , σ √ n Section 7.1 6 Estimating σ • When σ is unknown, we estimate it with the sample standard deviation s ....
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This note was uploaded on 04/02/2008 for the course STAT 226 taught by Professor Abbey during the Spring '08 term at Iowa State.
- Spring '08