An aquaculture farm takes water from a stream and returns it after it has circulated through the ?sh tanks. In order to ?nd out how much organic matter is left in the waste water after the circulation, some samples of the water are taken at the intake and other samples are taken at the downstream outlet and tested for biochemical oxygen demand (BOD). BOD is a common environmental measure of the quantity of oxygen consumed by microorganisms during the decomposition of organic matter. If BOD increases, it can be said that the waste matter contains more organic matter than the stream can handle. The following table gives data for this problem.
|
Upstream
|
9.0
|
6.8
|
6.5
|
8.0
|
7.7
|
8.6
|
6.8
|
8.9
|
7.2
|
7.0
|
|
Downstream
|
10.2
|
10.2
|
9.9
|
11.1
|
9.6
|
8.7
|
9.6
|
9.7
|
10.4
|
8.1
|
Assuming that the samples come from a normal distribution,
(a) Test that the mean BOD for the downstream samples is less than for the samples upstream at α = 0.05. Assume that the variances are equal.
(b) Test for the equality of the variances at α = 0.05.
(c) In parts (a) and (b), we assumed samples are independent. Now, we feel this assump- tion is not reasonable. Assuming that the difference of each pair is approximately normal, test that the mean BOD for the downstream samples is less than for the upstream samples at α = 0.05.