Given the two hypotheses H 0 : = 400 H 1 : = 415 and

Given the two hypotheses

H₀: μ = 400
H₁: μ = 415

and σ² = 1000 (for both hypotheses):

(a) Draw the distribution of e under both hypotheses.

(b) If the decision rule is chosen to be: reject H₀ if e ≥ 410 from a sample of size 40, find the probability of a Type II error and the power of the test.

(c) What happens to these answers as the sample size is increased? Draw a diagram to illustrate.