To evaluate the effect of a treatment, a sample of n = 9 is obtained from a population with a mean of μ = 40, and the treatment is administered to the individuals in the sample. After treatment, the sample mean is found to be M = 33.
a. If the sample has a standard deviation of s = 9, are the data sufficient to conclude that the treatment has a significant effect using a two-tailed test with α = .05?
b. If the sample standard deviation is s = 15, are the data sufficient to conclude that the treatment has a significant effect using a two-tailed test with α = .05?
c. Comparing your answer for parts a and b, how does the variability of the scores in the sample influence the outcome of a hypothesis test?