The quantity of dissolved oxygen is a measure of water pollution in lakes, rivers, and streams. Water samples were taken at four different locations in a river in an effort to determine if water pollution varied from location to location. Location I was 500 meters above an industrial plant water discharge point and near the shore. Location II was 200 meters above the discharge point and in midstream. Location III was 50 meters downstream from the discharge point and near the shore. Location IV was 200 meters downstream from the discharge point and in midstream. The following table shows the results. Lower dissolved oxygen readings mean more pollution. Because of the dif­ficulty in getting midstream samples, ecology students collecting the data had fewer of these samples. Use an a = 0.05 level of signifi­cance. Do we reject or not reject the claim that the quantity of dissolved oxygen does not vary from one location to another?

In the problem, please provide the following information.

(a) What is the level of signifi­cance? State the null and alternate hypotheses.

(b) Find SS_TOT, SS_BET, and SSW and check that SS_TOT – SSB_ET + SS_W. Find d.f._BET, d.f._W, MS_BET, and MS_W. Find the value of the sample test statistic F (F ratio).

What are the degrees of freedom?

(c) Find (or estimate) the P-value of the sample test statistic.

(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis?

(e) Interpret your conclusion in the context of the application.

(f) Make a summary table for your ANOVA test.

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Location I 7.3 6.9 7.5 6.8 6.2 Location II 6.6 7.1 7.7 8.0 Location III 4.2 5.9 4.9 5.1 4.5 Location IV 4.4 5.1 6.2