Notation Population Sample Call the variable we measure x1 in the first opulation and X2 in the second because the variable may have different distributions in the two populations. Notation used to nX S1 describe the two populations Population Variable Mean To do inference about the difference u-u between the means of the two populations x2 12 we start from the difference x-x between the means of the two samples There are 4 unknown parameters, the two means and the two standard TWo-sample t procedures deviations. We want to compare the two population means, either by giving a Standardize the observed diference x-x2l confidence interval for their difference by dividing by its standard deviation which A-H2 or by testing the hypothesis of no difference, Ho:#=u We use the sample means and standard h112 deviations to estimate the unknown parameters Notation used to describe the samples25 49 Notation • Call the variable we measure X1 in the first population and X2 in the second because the variable may have different distributions in the two populations. Notation used to describe the two populations: 2 1 Standard deviation Population Variable Mean 1 x 2 x μ1 μ2 σ 2 σ1 50 • There are 4 unknown parameters, the two means and the two standard deviations. We want to compare the two population means, either by giving a confidence interval for their difference or by testing the hypothesis of no difference, . • We use the sample means and standard deviations to estimate the unknown parameters. Notation used to describe the samples: 01 2 H : μ = μ μ1 2 − μ 26 51 2 1 Sample standard deviation Sample mean Sample size Population 1 n 2 n 1 x 2 x 1s 2 s To do inference about the difference between the means of the two populations, we start from the difference between the means of the two samples μ1 2 − μ 1 2 x − x 52 Two-sample t procedures • Standardize the observed difference by dividing by its standard deviation which is 1 2 x − x 2 2 1 2 1 2 n n σ σ +