Q1) Test effectiveness of a treatment, a sample of n=25 people is selected from normal population with a mean of μ=60. After treatment is administered to individuals in sample, the sample mean is found to be M = 55.

a) If population standard deviation is σ=10, can you conclude that treatment has significant effect? Use two-tailed test with α = 0.05.

b) If population standard deviation is σ=20, can you conclude that treatment has a significant effect? Use two-tailed test with α = 0.05.

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

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