A researcher studies water clarity at the same location in a lake on the same da
ID: 3172130 • Letter: A
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. Why is it important to take the measurements on the same date? Those are the same dates that all biologists use to take water clarity samples. Using the same dates maximizes the difference in water clarity. Using the same dates makes it easier to remember to take samples. Using the same dates makes the second sample dependent on the first. Does the evidence suggest that the clarity of the lake is improving at the alpha = 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.Explanation / Answer
Part a
Answer:
D. Using the same dates makes the second sample dependent on the first.
(Second sample observations should be based first sample observations for the paired t test for the population mean.)
Part b
Here, we have to use paired t test.
H0: µ1=µ2 versus Ha: µ1 µ2
Test statistic = Dbar/[Sd/sqrt(n)]
Where, n is sample size.
Calculation table for this test is given as below:
Before
After
Di
(Di - DBar)^2
65.2
62.6
2.6
30.06694444
61.7
60.6
1.1
15.86694444
42.8
51.4
-8.6
32.68027778
63.5
68.7
-5.2
5.366944444
70.2
76.6
-6.4
12.36694444
67.4
68.2
-0.8
4.340277778
DBar
-2.88333
We are given
Sample Size
6
DBar
-2.8833
Degrees of Freedom
5
SD
4.4875
Standard error = Sd/sqrt(n)
Standard error = 4.4875/sqrt(6) = 1.8320
Test statistic = -2.8833/1.8320
Test statistic = -1.573853712
P-value = 0.1763
Alpha value = 0.05
P-value > Alpha value
So, we do not reject the null hypothesis H0
Before
After
Di
(Di - DBar)^2
65.2
62.6
2.6
30.06694444
61.7
60.6
1.1
15.86694444
42.8
51.4
-8.6
32.68027778
63.5
68.7
-5.2
5.366944444
70.2
76.6
-6.4
12.36694444
67.4
68.2
-0.8
4.340277778
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