20. The analyses you have done on the Pre-test vs. Post-test data from the study of the effectiveness of Ginko supplements to enhance memory include the paired t-test, sign test, two-sample t-test, and the Mann-Whitney U-test. You have summarized the results from these analyses in the Table below. Test of Effect Size Standard Error of the Conclusion Significance (From Summary Sampling Distribution p-Value Effective? (Y/N) Reports) Paired t-test D= S D= 2-sample ( Xr - X) = S(XT - X) = t-test Sign test me = * * * * * * * * * * * * * *1 M-W U-test ( ma ma) = * * * * * * * * * * * * * a. Given the nature of the study design and the resulting data, only the paired t-test is appropriate. Explain WHY this is the most appropriate test. b. Compare the outcomes (Effect size, Standard error, p-values and conclusions) from the paired t-test and the two-sample t-test. Which of these t- tests do you think has greater statistical power? Explain WHY one test is more powerful than the other. c. Compare the results (p-values, conclusions) from the paired t-test vs. the sign test. Compare the results from the 2-sample t-test to the M-W U-test. Which type of test had greater power, parametric or non-parametric. What is the reason for this greater power? Explain your answer based on the descriptions of these tests in the book. d. A common mistake made by inexperienced scientists is that they choose a test of significance that is less than optimal or outright invalid for their particular study and data. Based on the comparisons of results in the Table above, describe the consequences of choosing an inappropriate test