Question

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
7.5	6.1	4.3	4.7
6.1	7.2	5.4	5.3
7.8	7.8	4.9	6.1
6.8	7.9	5.5
6.5		4.1

(b) Find SS_TOT, SS_BET, and SS_W and check that SS_TOT = SS_BET + SS_W. (Use 3 decimal places.)

SSTOT	=
SSBET	=
SSW	=

Find d.f._BET, d.f._W, MS_BET, and MS_W. (Use 3 decimal places for MS_BET, and MS_W.)

dfBET	=
dfW	=
MSBET	=
MSW	=

Find the value of the sample F statistic. (Use 3 decimal places.)


What are the degrees of freedom?
(numerator)=
(denominator)=

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

Source of Variation	Sum of Squares	Degrees of Freedom	MS	F Ratio	P Value	Test Decision
Between groups					---Select--- p-value > 0.100 0.050 < p-value < 0.100 0.025 < p-value < 0.050 0.010 < p-value < 0.025 0.001 < p-value < 0.010 p-value < 0.001	---Select--- Do not reject H0. Reject H0.
Within groups
Total

Answer 1

Solution:

We can use the excel ANOVA: Single Factor to answer the given questions. The excel output is given below:

Anova: Single Factor
SUMMARY
Groups	Count	Sum	Average	Variance
Location I	5	34.7	6.940	0.493
Location II	4	29	7.250	0.683
Location III	5	24.2	4.840	0.398
Location IV	3	16.1	5.367	0.493
ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
Between Groups	18.364	3	6.121	12.056	0.000	3.411
Within Groups	6.601	13	0.508
Total	24.965	16