Stat 226 - Section 6.1

# Stat 226 - Section 6.1 - Chapter 6 Introduction to...

This preview shows pages 1–3. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

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....
View Full Document

## 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.

### Page1 / 6

Stat 226 - Section 6.1 - Chapter 6 Introduction to...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online