A randomized experiment investigates whether an herbal treatment is better than a placebo in treating subjects suffering from depression. Unknown to the researchers, the herbal treatment has no effect: Subjects have the same score on a rating scale for depression (for which higher scores represent worse depression) no matter which treatment they take.
a. The study will use eight subjects, numbered 1 to 8. Using random numbers, pick the four subjects who will take the herbal treatment. Identify the four who will take the placebo.
b. After taking the assigned treatment for three months, subjects€™ results on the depression scale are as follows: Subject Response Subject Response Subject Response Subject Response

Based on the treatment assignment in part a, find the sample mean response for those who took the herbal supplement and for those who took the placebo.
c. Using the means in part b, explain how (i) sample means can be different even when there is €œno effect€ in a population of interest, and (ii) a difference between two sample means may not be €œstatistically significant€ even though those sample means are not equal.

Transcribed Image Text:

SuhjectResponse Subject ResponseSubject Response Subject Response 85 69 60 78 95 50 75