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5) The following data on nitrate concentrations was collected at specific points

ID: 3074467 • Letter: 5

Question

5) The following data on nitrate concentrations was collected at specific points along the same stream before and after a potential pollution source was established on the banks of the stream. Sample1 2 4 10 Point Time 1 4.977.399.089.65 9.8310.84 10.86 10.93 11.78 12.01 Time 22.92 5.98 6.75 7.72 11.98 14.07 14.65 14.94 17.8019.52 Use R to calculate: a) a paired sample t-test, b) a Wilcoxon Signed-Rank test Show the R syntax and results for each procedure in your write-up. Additionally, interpret the results of each test. In your write-up describing and interpreting the results of each test, specify the value of each test statistic, the null-hypothesis tested by each statistic, whether or not you rejected the null-hypothesis, and what assumptions of the tests might not have been met. Why couldn't you have used these tests in problem 4?

Explanation / Answer

> time1<-c(4.97,7.39,9.08,9.65,9.83,10.84,10.86,10.93,11.78,12.01)
> time2<-c(2.92,5.98,6.75,7.72,11.98,14.07,14.65,14.94,17.80,19.52)
> time1
[1] 4.97 7.39 9.08 9.65 9.83 10.84 10.86 10.93 11.78 12.01
> time2
[1] 2.92 5.98 6.75 7.72 11.98 14.07 14.65 14.94 17.80 19.52

> t.test(time1,time2,alternative="two.sided",paired=TRUE)

Paired t-test

data: time1 and time2

t = -1.6625, df = 9, p-value = 0.1308

alternative hypothesis: true difference in means is not equal to 0

95 percent confidence interval:

-4.4829087 0.6849087

sample estimates:
mean of the differences

-1.899

> wilcox.test(time1,time2,alternative="two.sided",paired=TRUE)

Wilcoxon signed rank test

data: time1 and time2

V = 11, p-value = 0.1055

alternative hypothesis: true location shift is not equal to 0

Paired T-test

Ho: The mean difference between nitrate concentration in stream is same after a potential pollution
H1: The mean difference between the nitrate concentration in stream is not same after potential pollution

We have used R to test and the code and results are already provided above.
According to the result the p- value is greater than 0.05 (0.1055) hence we donot reject our Ho and conclude that the mean difference between nitrate concentration is same after a potential pollution.
The test statistic obtained is -1.6625 and we have tested our hypothesis at 5% level of significance.

Wilcox signed Rank test

Ho: The median difference between nitrate concentration in stream is same after a potential pollution
H1: The median difference between the nitrate concentration in stream is not same after potential pollution

We have used R to test and the code and results are already provided above.
According to the result the p- value is greater than 0.05 (0.1308) hence we donot reject our Ho and conclude that the median difference between nitrate concentration in stream is same after a potential pollution.
We have tested our hypothesis at 5% level of significance.

Since the stream is always flowing the samples collected might not be the same as the sample collected earlier. There might be a chance that an entirely different sample is collected.

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