Qusetion: A quantification of coastal water quality converts measurements on several pollutants (arsenic in oyster shells, mercury, etc.) to a water quality index with values from 1 to 10. An investigation into the after-clean-up water quality of a lake analyzes water samples collected from five areas encompassing the two beaches on the eastern shore and the three beaches on the western shore. Let µ1 and µ2 denote the mean water quality index for the beaches on the eastern shore, and µ3, µ4, and µ5 be the mean water quality index for the beaches on the western shore.

(a) Write the contrasts that represent the effects of each of the five areas.

(b) Write the contrast for comparing the water quality around the two beaches on the eastern shore with that around the three beaches on the western shore.