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) and (c) below.

(a) Why is it important to take the measurements on the same date?

A. Those are the same dates that all biologist use to take water clarity samples.

B. Using the same dates makes the second sample dependent on the first and reduces variability in water clarity attributable to date.

C. Using the same dates maximizes the difference in water clarity.

D. Using the same dates makes it easier to remember to take samples.

(b) Does the evidence suggest that the clarity of the lake is improving at the a= 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.

Choose the conclusion below.

Let di=xi-yi Identify the null and alternative hypotheses

Determine the test statistic for this hypotheses test

_____ Round to two decimal places

Find the critical value for this hypothesis test

_____ ( use comma to separate as needed)

C. Draw a boxplot of the differenced data.

Does this visual evidence support the results obtained in part (b)?

A.Yes because the boxplot shows no ouliers

B. No because 0 is not contained in the boxplot

C. No because the boxplot is too large

D. Yes because 0 is contained in the boxplot.