5.19 In a trial of two types of rain gauge, 69 of type A and 12 of type B were distributed at random over a small area. In a certain period 14 storms occurred, and the average amounts of rain recorded for each storm by the two types of gauge are shown below. Another user claims to have found that the type B gauge gives consistently higher average readings than type A. Do these results substantiate such a conclusion? Investigate using two different nonparametric test procedures by finding the P value from

(a) Tables of the exact distribution

(b) Large sample approximations to the exact distributions Storm Type A Type B Storm Type A Type B 1 1.38 1.42 8 2.63 2.69 2 9.69 10.37 9 2.44 2.68 3 0.39 0.39 10 0.56 0.53 4 1.42 1.46 11 0.69 0.72 5 0.54 0.55 12 0.71 0.72 6 5.94 6.15 13 0.95 0.90 7 0.59 0.61 14 0.55 0.52 A total of four tests are to be performed. Discuss briefly the advisability of using nonparametric versus parametric procedures for such an investigation and the relative merits of the two nonparametric tests used. Discuss assumptions in each case.