Assume that a random sample of size 25 is to be taken from a normal population with μ = 10 and σ = 2. The value of μ, however, is not known by the person taking the sample. (a) Suppose that the person...

Assume that a random sample of size 25 is to be taken from a normal population with μ = 10 and σ = 2. The value of μ, however, is not known by the person taking the sample.

(a) Suppose that the person taking the sample tests H₀:μ = 10:4 against H₁:μ
 10:4. Although this null hypothesis is not true, it may not be rejected, and a type II error may therefore be committed. Compute β if α = 0:05.

(b) Suppose the same hypothesis is to be tested as that of part (a) but α = 0:01. Compute β.

(c) Suppose the person wanted to test H₀:μ = 11:2 against H₁: μ
 11:2. Compute β for α = 0:05 and α = 0:01.

(d) Suppose that the person decided to use H₁:μ
 11:2. Calculate β for α = 0:05 and α = 0:01.

(e) What principles of hypothesis testing are illustrated by these exercises?