1. Under what circumstances a 6 - point treatment effect can be very large, and in some circumstances it can be very small. Assume a sample of n = 16 individuals is selected from a population with a mean of µ = 70. A treatment is administered to the sample and, after treatment, the sample mean is found to be M = 76. Notice that the treatment appears to have increased scores by an average of 6 points.
a) If the population standard deviation is σ = 20 is the 6 point effect large enough to be statistically significant? Use the two - tailed test with α = .05
b) If the population standard deviation is σ = 8 is the 6-point effect large enough to be statistically significant? Use the two - tailed effect with α = .05
2. A researcher is evaluating the influence of a treatment using a sample selected from a normally distributed population with a mean of µ = 80 and a standard deviation of σ = 20. The researcher expects a 12 point treatment effect and plans to use a two-tailed hypothesis test with u α = .05
a. Compute the power of the test if the researcher uses a sample of n = 16 individuals.
b. Compute the power of the test if the researcher uses a sample of n = 25 individuals.