Question

4 A researcher studies water clarity of the same location in a lake on the same dates during the course of a year and repeat the measurements on the same dates 5 years later. The researcher immerses a weighted disk parted back and white and measure the depth (in inches) at which it is no longer vible. The collected data is given in the table below. Complete parts (a) through (c) below Observation 1 2 3 5 60 Date 1125 3/195/30 13 13 111 Initial Depth, X 449 614 413 729 353 695 Depth Five Years LaY 13.1 609 380 746 300 73.3 a) Why is it important to take the measurements on the same date? OA. Using the same dates makes the second sample dependent on the first and reduces variability in water clarity atributable to date OB. Using the same date maximizes the difference in water clarity OC. Using the same dates makes it easier to remember to take samples OD. Those we the same dates that all bologists use to take water clarity samples Does the widence suggest that the durity of the lake is improving the 0.05 level of significance ? Note that the normal probability plot and boxplot of the data indicate that the cances are approximately normally distributed with no others Let X - Y Wely the null and alternative hypotheses Н.

Answer 1

X	Y	Difference
44.9	43.1	1.8
61.4	60.9	0.5
41.3	38	3.3
72.9	74.6	-1.7
35.3	30	5.3
69.5	73.3	-3.8

∑d = 5.4

∑d² = 59.8

n = 6

Mean , x̅d = Ʃd/n = 5.4/6 = 0.9

Standard deviation, sd = √[(Ʃd² - (Ʃd)²/n)/(n-1)] = √[(59.8-(5.4)²/6)/(6-1)] = 3.3148

a)

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

b)

Null and Alternative hypothesis:

Ho : µd = 0

H1 : µd < 0

Test statistic:

t = (x̅d)/(sd/√n) = (0.9)/(3.3148/√6) = 0.67

df = n-1 = 5

p-value = T.DIST(0.67, 5, 1) = 0.732

Do not reject Ho. There is not sufficient evidence at the alpha = 0.05 level of significance to conclude that the clarity of the lake is improving.

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Answer C. Yes, because the boxplot supports that the lake is not becoming more clear, since most difference are positive or near 0.