a. Show for the upper-tailed test with σ1 and σ2 known that as either m or n increases,...

a. Show for the upper-tailed test with σ₁ and σ₂ known that as either m or n increases, β decreases when .

b. For the case of equal sample sizes (m = n) and fixed α , what happens to the necessary sample size n as β is decreased, where β is the desired type II error probability at a fixed alternative?