To evaluate the effect of a treatment, a sample is obtained from a population with a mean of µ = 30, and the treatment is administered to the individuals in the sample. After treatment, the sample mean is found to be µ = 31.3 with a standard deviation of s = 3.
a. If the sample consists of n = 16 individuals, are the data sufficient to conclude that the treatment has a significant effect using a two-tailed test with a = .05?
b. If the sample consists of n = 36 individuals, are the data sufficient to conclude that the treatment has a significant effect using a two-tailed test with a = .05?
c. Comparing your answer for parts a and b, how does the size of the sample influence the outcome of a hypothesis test?