A researcher studies water clarity at the same location in a lake on the same da

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) and (b) below. Observation 1 2 3 4 5 6 Date 1/25 3/19 5/30 7/3 9/13 11/7 Initial 51.4 62.7 59.9 40.7 40.6 37.6 After five years 52.2 60.1 61.7 44.3 44.9 44.1 (a) Why is it important to take the measurements on the same date? A. Those are the same dates that all biologists use to take water clarity samples. B. Using the same dates makes it easier to remember to take 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 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. Choose the correct conclusion below. Do not reject Upper H 0 . Reject Upper H 0 .

Explanation / Answer

The statistical software output for this problem is:

Paired T hypothesis test:
D = 1 - 2 : Mean of the difference between Initial and After 5 Years
H0 : D = 0
HA : D 0
Hypothesis test results:

Hence,

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

Since p - value is greater than 0.05, do not reject Ho.

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