A well-known conglomerate claims that its detergent "whitens and brightens better than all the rest." In order to compare the cleansing action of the top three detergents, 15 swatches of white cloth were soiled with red wine and grass stains and then washed in front-loading machines with the respective detergents. The following whiteness readings are shown in the accompanying table.

Detergent 1........................ Detergent 2........................... Detergent 3

84............................................... 78........................................ 87

79............................................... 74....................................... 80

87............................................... 81....................................... 91

85............................................... 86....................................... 77

94............................................... 86....................................... 78

a. Specify the competing hypotheses to test whether some differences exist in the median cleansing action of the three detergents.

b. Calculate the value of the test statistic H.

c. Approximate the p-value.

d. At the 1% significance level, do some differences exist between the median cleansing action by detergent? Explain.