Assume that you have a sample of n1 = 8, with the sample mean 1 = 42, and a sample standard deviation S1 = 4, and you have an independent sample of n2 = 15 from another population with a sample mean of 2 = 34 and a sample standard deviation S2 = 5.
a. What is the value of the pooled-variance tSTAT test statistic for testing H0: μ1 = μ2?
b. In finding the critical value, how many degrees of freedom are there?
c. Using the level of significance α = 0.01. what is the critical value for a one-tail test of the hypothesis H0: μ1 ≤ μ2 against the alternative, H1: μ1 > μ2?
d. What is your statistical decision?