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. In each of these two scenarios we distinguish between few cases… week 6

Case 1 – Variances are known Two independent populations, both normal variances known. week 6

Case 2 – Variances are known and equal Two independent populations, both normal variances known and equal. week 6

Case 3 – Variances unknown and equal Two independent populations, both normal variances equal but unknown. week 6

Case 4 – Large Samples Two independent populations, variances are equal but unknown, large samples. week 6

Case 5 – Large Samples Two independent populations, variances are unknown, large samples. week 6

Summary week 6

Examples week 6

Special case: Binomial Proportions Need large samples for CLT results… Example: week 6

One Sample Variance In many case we will be interested in making inference about the population variance. Suppose X1, X2,…,Xn are random sample from N(μ, σ2) where both μ and σ are unknown. A CI for σ2 is … week 6

Example week 6

Two Sample Variance In many case we will be interested in comparing the variances of two independent populations. week 6

Example week 6