1. Class 3 Comparing Two Population Means— Pooled-t Test and Paired-t Test

2. Tests for (  1 -  2 ) when  1 and  2 are Unknown: The Pooled t-test As was the case in the t-test, we have to get an estimate(s) of our unknown variance(s) (  1 2 and  2 2 ). Where will we get them? Extra assumptions required for this test: (1) Sampling from normal distributions. (2) Samples are simple random samples. (3)  1 2 =  2 2.

3. Pooled t-test (cont.) EXCEL supports this through tools/data analysis/t-Test: Two-Sample Assuming Equal Variances. Note that if equal variance assumption looks suspicious, you can use tools/data analysis/t-Test: Two-Sample Assuming Unequal Variances. You can test variance equality by tools/data analysis/F-Test Two-Sample for Variances.

4. Matched Samples: The Paired t-test Two population problem that is reduced to a single population problem by the method of collecting data. EXCEL supports this by tools/data analysis/t-Test: Paired Two Sample for Means.