In a study of methods of producing sheep's milk for use in cheese manufacture, ewes were randomly allocated to either a mechanical or a manual milking method. The investigator suspected that the mechanical method might irritate the udder and thus produce a higher concentration of somatic cells in the milk. The accompanying data show the average somatic cell count for each animal.

(a) Do the data support the investigator's suspicion? Use a t test against a directional alternative at α = 0.05. The standard error of (1 - 2) is SE = 427.54 and formula (6.7.1) yields 9.2 df.
(b) Do the data support the investigator's suspicion? Use a Wilcoxon-Mann-Whitney test against a directional alternative at α = 0.05. (The value of the Wilcoxon-Mann-Whitney statistic is Us = 69.) Compare with the result of part (a).
(c) What condition is required for the validity of the t test but not for the Wilcoxon-Mann-Whitney test? What features of the data cast doubt on this condition?
(d) Verify the value of Us given in part (b).

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Somatic count (10, × cells/ml) Mechanical milking Manual milkin 186 107 2,966 269 59 65 126 123 164 408 324 548 139 10 219.0 156.2 1,887 3,452 189 93 618 130 2,493 10 Mean 1215.6 SD 1,342.9