1. week 111 Review - Sum of Normal Random Variables The weighted sum of two independent normally distributed random variables has a normal distribution. Example

2. week 112 Two Sample Problem Sometimes we will be interested in comparing means in two independent populations (e.g. mean income for male and females). We consider two basic scenarios: populations are normal or populations are not normal but the sample sizes are large.

3. week 113 CI for Difference between Two Means – Case I Suppose we have two independent large random samples from two different populations and we are interested in comparing the means of these two populations. The confidence interval for the difference between two means in this case is…

4. week 114 Example

5. week 115 Tests for Difference between Two Means Suppose we have two independent large random samples from two different populations. We are interested in testing H 0 : μ x - μ y = δ versus a one sided or a two sided alternative… Then….

6. week 116 Example

7. week 117 Minitab CI and Hypothesis Tests for Two Means We can use Minitab to construct confidence intervals, conduct hypothesis tests, for the difference between two means, two independent large iid samples. The command in Minitab is Stat  basic statistic  2 sample t  complete dialogue box  o.k. Note that the data can be in two different columns or in one column with another column denoting the population of each observation. We can also use Minitab to calculate the power of the two sample hypothesis test. The command in Minitab is Stat  power and sample size  2 sample t  complete dialogue  o.k