1) Assume these two data sets are unpaired and independent of each other: X: 33 41 49 25 37 37 Y: 46 45 39 52 38 38 a) Calculate a pooled estimate of the common population variance needed for Student's t-test. b) Perform Student's t-test. Report the value of the test statistic; the critical value; and your reject / do not reject decision regarding the null of equal population means. 2) If you had performed Welch's t-test in the previous problem, what would the test statistic have been? 3) If the data in the first problem had been paired, how many degrees of freedom would the corresponding t-test have had? 4) If there are n=20 and m=10 values and W is the test statistic of the rank sum test... a) What is the smallest that W could be? b) What is the largest that W could be? c) What transformation of W would have a standard Normal distribution under the null?