1. When is the t-test statistic used in a hypothesis test for the difference between two means?
2. Given a sample of size n1 = 40 from a population with a standard deviation σ1 = 20, and an independent sample of size n2 = 50 from another population with a known standard deviation σ2 = 10, what is the value of z-stat when testing for the difference in two population means if x1 = 72 and x2 = 66?
3. When conducting a two-tailed test for equality of means, what is the t-crit value:
(a) when n1 = 14,n2 = 26 and α = 0.05?
(b) when n1 = 54, n2 = 38 and α = 0.05?