An experiment was conducted to compare the length of time it takes a person to recover from each of the three types of influenza-Victoria A, Texas, and Russian. Twenty-one human subjects were selected at random from a group of volunteers and divided into three groups of 7 each. Each group was randomly assigned a strain of the virus and the influenza was induced in the subjects. All of the subjects were then cared for under identical conditions, and the recovery time (in days) was recorded. The ranks of the results appear in the following table.
Victoria A Texas Russian
20 14.5 9
6.5 16.5 1
21 4.5 9
163 2.5 4.5
12 14.5 6.5
18.5 12 2.5
9 18.5 12
a. Do the data provide sufficient evidence to indicate that the recovery times for one (or more) type(s) of influenza tend(s) to be longer than for the other types? Give the associated p-value.
b. Do the data provide sufficient evidence to indicate a difference in locations of the distributions of recovery times for the Victoria A and Russian types? Give the associated p-value.