A random sample is selected from a normal population with a mean of m = 50 and a standard deviation of s = 12. After a treatment is administered to the individuals in the sample, the sample mean is found to be M = 55.
a. If the sample consists of n = 16 scores, 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 sample consists of n = 36 scores, 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 size of the sample influences the outcome of a hypothesis test.