The Department of Natural Resources (DNR) received a complaint from recreational fishermen that a community was releasing sewage into the river where they fished. These types of releases lower the level of dissolved oxygen in the river and hence cause damage to the fish residing in the river. An inspector from the DNR designs a study to investigate the fishermen's claim. Fifteen water samples are selected at locations on the river upstream from the community and fifteen samples are selected downstream from the community. The dissolved oxygen readings in parts per million (ppm) are given in the following table.

Upstream 5.2 4.8 5.1 5.0 4.9 4.8 5.0 4.7 4.7 5.0 4.6 5.2 5.0 4.9 4.7 Downstream 3.2 3.4 3.7 3.9 3.6 3.8 3.9 3.6 4.1 3.3 4.5 3.7 3.9 3.8 3.7

a. In order for the discharge to have an impact on fish health, there needs to be at least an .5 ppm reduction in the dissolved oxygen. Do the data provide sufficient evidence that there is a large enough reduction in the mean dissolved oxygen between the upstream and downstream water in the river to impact the health of the fish? Use a = .01.

b. Do the required conditions to use the test in part (a) appear to be valid?

c. What is the level of significance of the test in part (a)?

d. Estimate the size of the difference in the mean dissolved oxygen readings for the

two locations on the river using a 99% confidence interval.