A Vedic mathematician introduces a new method to add number quickly. The mathematician plans to promote his new method to parents. He selected a group of 9 students (Group X) and trained them his method and selected randomly another group of 11 students (Group Y) who did not exposed to his method. The students were asked to solve an addition problem and the time (in seconds) taken by the students to solve the problem were recorded as the table below.
(a) Complete the rank for Mann-Whitney test [4m]
(b) Compute the mean and standard deviation of the sum of the rank [4m]
(c) Determine if the new method is quicker to solve addition problem as claimed by the mathematician. [8m]
18 21 16 22 19 25 20 24 24
20 17 25 29 16 20 20 27 31 18 25