tailieunhanh - Lecture Business statistics in practice (7/e): Chapter 11 - Bowerman, O'Connell, Murphree

Chapter 11 - Statistical inferences for population variances. After mastering the material in this chapter, you will be able to: Explain the basic terminology and concepts of experimental design, compare several different population means by using a one-way analysis of variance, compare treatment effects and block effects by using a randomized block design,. | Statistical Inferences for Population Variances Chapter 11 Copyright © 2014 by The McGraw-Hill Companies, Inc. All rights reserved. McGraw-Hill/Irwin Statistical Inferences for Population Variances The Chi-Square Distribution Statistical Inference for a Population Variance The F Distribution Comparing Two Population Variances by Using Independent Samples 11- The Chi-Square Distribution Sometimes make inferences using the chi-square distribution Denoted ² Skewed to the right Exact shape depends on the degrees of freedom Denoted df A chi-square point ²α is the point under a chi-square distribution that gives right-hand tail area LO11-1: Describe the properties of the chi-square distribution and use a chi-square table. 11- Statistical Inference for Population Variance If s2 is the variance of a random sample of n measurements from a normal population with variance σ2 The sampling distribution of the statistic (n - 1) s2 / σ2 is a . | Statistical Inferences for Population Variances Chapter 11 Copyright © 2014 by The McGraw-Hill Companies, Inc. All rights reserved. McGraw-Hill/Irwin Statistical Inferences for Population Variances The Chi-Square Distribution Statistical Inference for a Population Variance The F Distribution Comparing Two Population Variances by Using Independent Samples 11- The Chi-Square Distribution Sometimes make inferences using the chi-square distribution Denoted ² Skewed to the right Exact shape depends on the degrees of freedom Denoted df A chi-square point ²α is the point under a chi-square distribution that gives right-hand tail area LO11-1: Describe the properties of the chi-square distribution and use a chi-square table. 11- Statistical Inference for Population Variance If s2 is the variance of a random sample of n measurements from a normal population with variance σ2 The sampling distribution of the statistic (n - 1) s2 / σ2 is a chi-square distribution with (n – 1) degrees of freedom Can calculate confidence interval and perform hypothesis testing 100(1-α)% confidence interval for σ2 LO11-2: Use the chi-square distribution to make statistical inferences about population variances. 11- Formulas LO11-2 11- F Distribution LO11-3: Describe the properties of the F distribution and use on F table. Figure 11- F Distribution Tables The F point F is the point on the horizontal axis under the curve of the F distribution that gives a right-hand tail area equal to The value of F depends on a (the size of the right-hand tail area) and df1 and df2 Different F tables for different values of Tables for = Tables for = Tables for = Tables for = LO11-3 11- Comparing Two Population Variances by Using Independent Samples Population 1 has variance σ12 and population 2 has variance σ22 The null hypothesis H0 is that the variances are the .