A random sample of n = 36 scores is selected from a normal population with a mean of µ = 60. After a treatment is administered to the individuals in the sample, the sample mean is found to be M = 52.

a. If the population standard deviation is σ = 18, is the sample mean sufficient to conclude that the treatment has a significant effect? Use a two-tailed test with α = .05.

b. If the population standard deviation is σ = 30, is the sample mean sufficient to conclude that the treatment has a significant effect? Use a two-tailed test with α = .05.

c. Comparing your answers for parts a and b, explain how the magnitude of the standard deviation influences the outcome of a hypothesis test.