To test the comparative brightness of two red dyes, nine samples of cloth were taken from a production line and each sample was divided into two pieces. One of the two pieces in each sample was randomly chosen and red dye 1 applied; red dye 2 was applied to the remaining piece. The following data represent a "brightness score" for each piece.
Sample 1 2 3 4 5 6 7 8 9
Dye 1 10 12 9 8 15 12 9 10 15
Dye 2 8 11 10 6 12 13 9 8 13
a. Is there sufficient evidence to indicate a difference in mean brightness scores for the two dyes? Use α = 0.05.
b. Find the approximate p-value for the test and interpret its value.