Question: A sample of n = 9 individuals was selected from a normally distributed population with a mean of µ = 25 and a standard deviation of σ = 6. A treatment was administered to the sample and, after treatment, the nine individuals produced the following scores: 36, 27, 30, 33, 22, 30, 30, 24, 38.

a. Calculate the sample mean.

b. Sketch a histogram showing the sample distribution.

c. Does the sample appear to be centered around µ = 25 or does the treatment appear to have moved the scores away from µ = 25?

d. Use a hypothesis test with α = .05 to determine whether the treatment had a significant effect.

e. Looking at the sample distribution from part b, determine how big the treatment effect is. Specifically, what is the distance between the sample mean and the original population mean?

f. Compute Cohen’s d to measure the size of the treatment effect.