Chapter 8.2（课件）- 《统计学基础（英文版）》同步教学（人民大学版）

Chapter Hypothesis Testing with Two Samples 8 1 Copyright 2019, 2015, 2012, Pearson Education, Inc. 1 Larson/Farber 6th ed Chapter 1 Chapter Outline 8.1 Testing the Difference Between Means (Independent Samples, 1 and 2 Known) 8.2 Testing the Difference Between Means (Independent Samples, 1 and 2 Unknown) 8.3 Testing the Difference Between Means (Dependent Samples) 8.4 Testing the Difference Between Proportions . 1 Copyright 2019, 2015, 2012, Pearson Education, Inc. Section 8.2 Testing the Difference Between Means (Independent Samples, 1 and 2 Unknown) . 1 Copyright 2019, 2015, 2012, Pearson Education, Inc. Section 8.2 Objectives How to perform a t-test for the difference between two means μ1 and μ2 with independent samples with 1 and 2 unknown . 1 Copyright 2019, 2015, 2012, Pearson Education, Inc. Two Sample t-Test for the Difference Between Means A two-sample t-test is used to test the difference between two population means μ1 and μ2 when σ2 and σ2 are unknown, the samples are random, the samples are independent, and the populations are normally distributed or both n1 ≥ 30 and n2 ≥ 30. . 1 Copyright 2019, 2015, 2012, Pearson Education, Inc. Two Sample t-Test for the Difference Between Means The static test is The standardized test statistic is s . t = 1 Copyright 2019, 2015, 2012, Pearson Education, Inc. The standard error for the sampling distribution of is Two Sample t-Test for the Difference Between Means Variances are equal: If the population variances are equal, then information from the two samples is combined to calculate a pooled estimate of the standard deviation . d.f.= n1 + n2 – 2 . = 1 Copyright 2019, 2015, 2012, Pearson Education, Inc. Variances are not equal: If the population variances are not equal, then the standard error is d.f = smaller of n1 – 1 or n2 – 1 Two Sample t-Test for the Difference Between Means . 1 Copyright 2019, 2015, 2012, Pearson Education, Inc. Two-Sample Tests for Independent Sample