Question

A researcher studies water clarity at the same location in a lake on the same dates during the course of a year and repeats the measurements on the same dates 5 years later. The researcher immerses a weighted disk painted black and white and measures the depth​ (in inches) at which it is no longer visible. The collected data is given in the table below. Complete parts​ (a) through​ (c) below.
Observation
1
2
3
4
5
6

Date
​1/25
​3/19
​5/30
​7/3
​9/13
​11/7
Initial​ Depth, Xi
46.1
69.5
48.5
60.8
59.7
74.5
Depth Five Years​ Later, Yi
53.0
68.8
53.4
62.9
65.5
75.9

​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 alpha equals 0.05 level of​ significance? Note that the normal probability plot and boxplot of the data indicate that the differences are approximately normally distributed with no outliers.
Let diequalsXiminusYi. Identify the null and alternative hypotheses.

Determine the test statistic for this hypothesis test.

Find the​ P-value for this hypothesis test.

Answer 1