A researcher is testing the effectiveness of a new herbal supplement that claims to improve physical fitness. A sample of n = 16 college students is obtained and each student takes the supplement daily for six weeks. At the end of the 6-week period, each student is given a standardized fitness test and the average score for the sample is M = 39.

If we know for the general population of college students, the distribution of test scores is normal with a mean of = 34 and a standard deviation of = 9. Do students taking the supplement have significant effect on fitness scores? Please conduct a two tailed test at = .05. (8 points)

Following question 1), compute the Cohen's d to estimate the effect size. (2 points)

If we don't know population's standard deviation, only know population mean = 34, but we measured sample's standard deviation is s=10, does the supplement have significant effect on fitness scores? Please conduct a two tailed test at = .05. (8 points)

Following question 3), calculate the Cohen's d to estimate the effect size. (2 points)