A random sample of n = 25 scores is selected from a normal population with a mean of µ = 40. After a treatment is administered to the individuals in the sample, the sample mean is found to be µ = 44.
a. If the population standard deviation is s = 5, is the sample mean sufficient to conclude that the treatment has a significant effect? Use a two-tailed test with a = .05.
b. If the population standard deviation is s = 15, is the sample mean sufficient to conclude that the treatment has a significant effect? Use a two-tailed test with a = .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.