《统计学基础（英文版·第7版）》教学课件les7e_ppt_08_02.pptxVIP

Chapter;Chapter Outline;Section 8.2;Section 8.2 Objectives;Two Sample t-Test for the Difference Between Means;Two Sample t-Test for the Difference Between Means;The standard error for the sampling distribution of  is ;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 Tests for Independent Samples;Two-Sample t-Test for the Difference Between Means (Independent Samples σ2 and σ2 Unknown );;;Example: Two-Sample t-Test for the Difference Between Means;Solution: Note that s1 and s2 are unknown, the samples are random and independent, and the populations are normally distributed. So, you can use the t-test. The claim is “there is a difference in the mean mathematics test scores for the students of the two teachers.” So, the null and alternative hypotheses are H0: m1 = m2 and Ha: m1 ? m2. (Claim);?;?;The figure shows the location of the rejection regions and the standardized test statistic t. Because t is not in the rejection region, you fail to reject the null hypothesis.;Example: Two-Sample t-Test for the Difference Between Means;Solution: s1 and s2 are unknown, the samples are random and independent, and both n1 and n2 are at least 30. So, you can use the t-test. The claim is “the mean driving cost per mile of the manufacturer’s sedans is less than that of its leading competitor.” So, the null and alternative hypotheses are H0: m1 ? m2 and Ha: m1 m2. (Claim);?;?;?;The figure shows the location of the rejection region and the standardized test statistic t. Because t is in the rejection region, you reject the null hypothesis.