Question

# A researcher studies water clarity at the same location in a lake on the same dates...

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 ​(b) below.

 Observation Date Initial After five years 1 2 3 4 5 6 ​1/25 ​3/19 ​5/30 ​7/3 ​9/13 ​11/7 39.5 46.6 55.4 62.2 40.5 39.1 40.8 48.9 51.7 70.7 36.1 47.4

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

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

B.Those are the same dates that all biologists use to take water clarity samples.

C.Using the same dates makes the second sample dependent on the first.

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

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

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