A Secchi disk is an 8-inch-diameter weighted disk that is painted black and white and attached to a rope. The disk is lowered into water and the depth (in inches) at which it is no longer visible is recorded. The measurement is an indication of water clarity. An environmental biologist is interested in determining whether the water clarity of the lake at Joliet Junior College is improving. She takes measurements at the same location on eight dates during the course of a year and repeats the measurements on the same dates 5 years later. She obtains the following results:

(a) Why is it important to take the measurements on the same date?
(b) Does the evidence suggest that the clarity of the lake is improving at the α = 0.05 level of significance?
(c) Draw a boxplot of the differenced data. Does this visual evidence support the results obtained in part (b)?

Observation 1 Date Initial depth, X 38 58 65 74 56 36 56 52 Depth 5 years later, Y 2 6 5/11 6/7 6/24 718 7127 8/31 9/30 10/12 52 60 72 72 54 48 58 60