Assume that you have a sample of n1 = 8, with the sample mean X₁ = 42, and a sample standard deviation σ₁ = 4, and you have an independent sample of n₂ = 15 from another population with a sample mean of X-bar₂ = 34 and a sample standard deviation σ₂ = 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?