For all hypothesis tests, you must show the four steps:

1. Hypotheses

2. Test statistic

3. p-value or p-value approximation

4. Conclusion sentence (Do no just say ”Reject the nullhypothesis” or ”Fail to reject the

null hypothesis”)

If doing the hypothesis test in jamovi, you must include thejamovi output but show the four

steps separately as well.

Exercises

1. The Department of Natural Resources (DNR) received acomplaint from recreational fishermen that

a community was releasing sewage into the river where theyfished. These types of releases lower the

level of dissolved oxygen in the river and hence cause damage tothe fish residing in the river. An

inspector from the DNR designs a study to investigate thefishermen’s claim. Fifteen water samples

are selected at locations on the river upstream from thecommunity and fifteen samples are selected

downstream from the community. The dissolved oxygen readings inparts per million (ppm) are given

in the following table.

Data available online: Ex 1 Data

Above

5.2

4.8

5.1

5.0

4.9

4.8

5.0

4.7

4.7

5.0

4.7

5.1

5.0

4.9

4.9

Below

4.2

4.4

4.7

4.9

4.6

4.8

4.9

4.6

5.1

4.3

5.5

4.7

4.9

4.8

4.7

(a) Perform a hypothesis test to test whether the mean oxygenlevels upstream (above) is unequal to

the mean oxygen content downstream (below). Use α = 0.01. (10points)

(b) Estimate the size of the difference in the mean dissolvedoxygen readings for the two locations on

the river using a 99% confidence interval. Assume σ1does not =σ2(5 points)

(c) Assuming σ1=σ2, estimate the size of the difference in themean dissolved oxygen readings for

the two locations on the river using a 99% confidence interval.(5 points)