Suppose that a researcher is interested in whether an exercise improves intelligence. The researcher randomly selects 100 participants, assigns them to an exercise program, and measures intelligence at the end of the exercise program. The measurement of intelligence has a known or assumed average score of μ = 100 and a known or assumed standard deviation of σ = 15 in the population.

a. What hypothesis test should the researcher use to evaluate whether the treatment affected intelligence?

b. If σ and σ² were unknown, what hypothesis test should be used?