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Unformatted text preview: Chapter 6 Introduction to Inference Chapter 6 1 Statistical Inference • The purpose of statistical inference is to draw conclusions from data. • Formal inference relies on probability theory to describe random variation. • Inference uses the properties of the sampling distribution outlined in Section 4.4 Chapter 6 2 Example - Commercial Preference • Two versions of a television commercial are both shown to a sample of 20 consumers. • Twelve who see the ads say they prefer the newer version and 8 prefer the older version. • Is the newer commercial more effective? • Possibly, but a difference this large or larger could occur by chance about 20% of the time. • In statistical inferences, we are especially interested in those outcomes that would be unlikely to occur by chance. Chapter 6 3 Responsible Use of Inference • It is important to understand the reasoning behind any statistical technique that is used in practice. • The elaborate and convenient machinery of statistical inference does not make up for poor study design. • Statistical inference requires the use of probability in the study. • In an observational study, individuals should be selected at random. • In an experiment, subjects are assigned to treatments randomly. • Use the tools of Chapters 1-3 and continue with formal statistical inference if it is appropriate for the current task. Chapter 6 4 Inference Basics • We will begin with some inference techniques for the unknown population mean μ . • To start, we will make the fairly unrealistic assumption that we know the population standard deviation σ . • Later topics in Statistics 226 will include more general procedures. • All of statistical inference uses the general ideas introduced in this chapter. Chapter 6 5 Section 6.1 Estimating with Confidence Section 6.1 6 Estimation of μ • Recall that the objective of statistical inference is to draw conclusions about the larger population based on the data from a sample . • The sample mean ¯ x is the natural estimator of the unknown population mean μ . • The sample mean ¯ x is an unbiased estimator under simple random sampling. • The Law of Large Numbers says that the sample mean approaches μ as the sample size increases. Section 6.1 7 Example - Accountant Salaries • A 2006 survey of 150 recent graduates with accounting degrees found that their mean starting salary was ¯ x = $ 46 , 200....
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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