Question: To test the effectiveness of a treatment, a sample of n = 25 people is selected from a normal population with a mean of µ = 60. After the treatment is administered to the individuals in the sample, the sample mean is found to be M = 55.

a. If the population standard deviation is σ = 10, can you conclude that the treatment has a significant effect? Use a two-tailed test with α = .05.

b. If the population standard deviation is σ = 20, can you conclude that the treatment has a significant effect? Use a two-tailed test with α = .05.

c. Compute Cohen’s d to measure effect size for both tests (σ = 20 and σ = 10).

d. Briefly describe how the standard deviation influences the outcome of the hypothesis test. How does σ influence measures of effect size?