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Stat 226 - Section 7.1

Stat 226 - Section 7.1 - Introduction Chapter 7 Inference...

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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
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Estimating σ When σ is unknown, we estimate it with the sample standard deviation s .
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