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 a 5% 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? Location I Location II Location III Location IV 7.6 6.3 4.6 4.2 6.1 7.8 5.1 5.6 7.7 7.5 4.5 6.9 6.9 8.4 5.5 6.1 4.4 (b) Find SSTOT, SSBET, and SSW and check that SSTOT = SSBET + SSW. (Use 3 decimal places.) SSTOT = SSBET = SSW = Find d.f.BET, d.f.W, MSBET, and MSW. (Use 3 decimal places for MSBET, and MSW.) dfBET = dfW = MSBET = MSW = Find the value of the sample F statistic. (Use 3 decimal places.) What are the degrees of freedom? (numerator) (denominator) ) Make a summary table for your ANOVA test. Source of Variation Sum of Squares Degrees of Freedom MS F Ratio Between groups Within groups Total
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 a 5% 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?
| Location I | Location II | Location III | Location IV |
| 7.6 | 6.3 | 4.6 | 4.2 |
| 6.1 | 7.8 | 5.1 | 5.6 |
| 7.7 | 7.5 | 4.5 | 6.9 |
| 6.9 | 8.4 | 5.5 | |
| 6.1 | 4.4 |
(b) Find SSTOT, SSBET, and SSW and check that SSTOT = SSBET + SSW. (Use 3 decimal places.)
| SSTOT | = | |
| SSBET | = | |
| SSW | = |
Find d.f.BET, d.f.W, MSBET, and MSW. (Use 3 decimal places for MSBET, and MSW.)
| dfBET | = | |
| dfW | = | |
| MSBET | = | |
| MSW | = |
Find the value of the sample F statistic. (Use 3 decimal places.)
What are the degrees of freedom?
(numerator)
(denominator)
) Make a summary table for your ANOVA test.
| Source of Variation |
Sum of Squares |
Degrees of Freedom |
MS | F Ratio |
||
| Between groups | ||||||
| Within groups | ||||||
| Total |
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