For each of the following pairs of hypotheses, determine whether each pair represents valid hypotheses for a hypothesis test. Explain reasons for any pair that is indicated to be invalid.
a. H0: μ = 15, HA: μ 7 15
b. H0: μ = 20, HA: μ ≠ 20
c. H0: μ 6 30, HA: μ > 30
d. H0: μ ≤ 40, HA: μ ≥ 40
e. H0: x ≤ 45, HA: x > 45
f. H0: μ ≤ 50, HA: μ > 55