Finding Critical Values ?Assume that we have two treatments (A and B) that produce quantitative results, and we have only two observations for treatment A and two observations for treatment B. We cannot use the test statistic given in this section because both sample sizes do not exceed 10. a.? Complete the accompanying table by listing the five rows corresponding to the other five cases, and enter the corresponding rank sums for treatment A. b.? List the possible values of ?R? and their corresponding probabilities. (Assume that the rows of the table from part (a) are equally likely.) c.? Is it possible, at the 0.10 significance level, to reject the null hypothesis that there is no difference between treatments A and B? Explain.
Solution 14BB Step 1 : Hypothesis: H 0 here is a difference between treatment A and B H 1 here is no difference between treatment A and B a) The completed table for treatment A is given below: Rank sum for Rank treatment A 1 2 3 4 A A B B 1+2=3 A B A B 1+3 = 4 A B B A 1+4 = 5 B B A A 3+4 = 7 B A B A 2+4 = 6 B A A B 2+3 = 5 Step 2 : b) The values of R are 3,4,5,5,6,7 and their corresponding probabilities are P(R) = The number of times the R appears The total number of R values 1 P(3) = 6 = 0.1666 0.1667 P(4) = 6 = 0.1667 P(5) = 2 = 0.333 6 P(6) = 1 = 0.1667 6 1 P(7) = 6 = 0.1667