Chapter 8.3（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 8.3 Testing the Difference Between Means (Dependent Samples) . 1 Copyright 2019, 2015, 2012, Pearson Education, Inc. Section 8.3 Objectives How to perform a t-test to test the mean of the difference for a population of paired data . 1 Copyright 2019, 2015, 2012, Pearson Education, Inc. The test statistic is the mean of these differences. t-Test for the Difference Between Means To perform a two-sample hypothesis test with dependent samples, the difference between each data pair is first found: d = x1 – x2 Difference between entries for a data pair Mean of the differences between paired data entries in the dependent samples . 1 Copyright 2019, 2015, 2012, Pearson Education, Inc. t-Test for the Difference Between Means Three conditions are required to conduct the test. The samples must be randomly selected. The samples must be dependent (paired). Both populations must be normally distributed or the number n of pairs of data is at least 30. If these conditions are met, then the sampling distribution for , the mean of the differences of the paired data entries in the dependent samples, is approximated by a t-distribution with n – 1 degrees of freedom, where n is the number of data pairs. . 1 Copyright 2019, 2015, 2012, Pearson Education, Inc. Symbols used for the t-Test for μd The number of pairs of data The difference between entries for a data pair, d = x1 – x2 The hypothesized mean of the differences of paired data in the population n d Symbol Description . 1 Co