Consider the following hypothesis test: H 0 : µ ≤ 50; H a : µ > 50. Given a sample size of 30, it is determined that ¯ x = 56. It is known that σ = 8. Let α = . 05 (d) Do you reject H 0 based on the...

Consider the following hypothesis test:
H0 :
µ ≤
50;
H
a
:
µ >
50. Given a sample size of 30, it is determined that ¯x
= 56. It is known that
σ
= 8. Let
α
=
.05

(d) Do you reject
H0 based on the evidence from the sample? What decision rule did you apply for your conclusion?

(e) Now suppose that
σ
is unknown. What distribution will now be relevant for statistical inference? Repeats parts (b), (c), and (d) when
s
= 10.