A researcher is testing the effectiveness of a new herbal supplements that claims to improve physical fitness. A sample of n=16 college students is obtained and each student takes the supplements 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

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

2) following question 1), computer the Cohen's d to estimate the effect size.

3. If we don't know the populations standard deviation, is s=10, does the supplement have significant effect on fitness scores? Please two tailed test at a =.05

4) following question 3), calculate the Cohens d to estimate the effect size.