A sample of n = 16 individuals is selected from a population with m = 30. After a treatment is administered to the individuals, the sample mean is found to be M = 33.
a. If the sample variance is s2 = 16, then conduct a hypothesis test to evaluate the significance of the treatment effect and calculate r2 to measure the size of the treatment effect. Use a two-tailed test with a = .05.
b. If the sample variance is s2 = 64, then conduct a hypothesis test to evaluate the significance of the treatment effect and calculate r2 to measure the size of the treatment effect. Use a two-tailed test with a = .05.
c. Describe how increasing variance affects the likelihood of rejecting the null hypothesis and the measure of effect size.