Chapter 10.3（课件）- 《统计学基础（英文版）》同步教学（人民大学版）

Chapter Chi-Square Tests and the F-Distribution 10 1 Copyright 2019, 2015, 2012, Pearson Education, Inc. 1 Larson/Farber 6th ed Chapter 1 Chapter Outline 10.1 Goodness-of-Fit Test 10.2 Independence 10.3 Comparing Two Variances 10.4 Analysis of Variance . 1 Copyright 2019, 2015, 2012, Pearson Education, Inc. Section 10.3 Comparing Two Variances . 1 Copyright 2019, 2015, 2012, Pearson Education, Inc. Section 10.3 Objectives How to interpret the F-distribution and use an F-table to find critical values How to perform a two-sample F-test to compare two variances . 1 Copyright 2019, 2015, 2012, Pearson Education, Inc. F-Distribution Let represent the sample variances of two different populations. If both populations are normal and the population variances are equal, then the sampling distribution of is called an F-distribution. . 1 Copyright 2019, 2015, 2012, Pearson Education, Inc. Properties of the F-Distribution The F-distribution is a family of curves each of which is determined by two types of degrees of freedom: The degrees of freedom corresponding to the variance in the numerator, denoted d.f.N The degrees of freedom corresponding to the variance in the denominator, denoted d.f.D The F-distributions is positively skewed and therefore the distribution is not symmetric. The total area under each F-distribution curve is equal to 1. . 1 Copyright 2019, 2015, 2012, Pearson Education, Inc. Properties of the F-Distribution All F-values are greater than or equal to 0. For all F-distributions, the mean value of F is approximately equal to 1. . 1 Copyright 2019, 2015, 2012, Pearson Education, Inc. 7 Larson/Farber 4th ed Chapter 10 Finding Critical Values for the F-Distribution Specify the level of significance α. Determine the degrees of freedom for the numerator, d.f.N. Determine the degrees of freedom for the denominator, d.f.D. Use Table 7 in Appendix B to find the critical value. If the hypothesis test is one-tailed, use the