Question

M14 #20: 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
7.2	6.2	4.9	4.4
6.4	7.5	5.3	5.4
7.1	7.9	4.7	6.1
6.3	7.9	5.5
6.9		4.6

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

B) Find d.f._BET, d.f._W, MS_BET, and MS_W. (Use 4 decimal places for MS_BET, and MS_W.)

C) Find the value of the sample F statistic. (Use 2 decimal places.)

Answer 1

Following tables shows the calculations:

	G1, I	G2, II	G3, III	G4, IV
	7.2	6.2	4.9	4.4
	6.4	7.5	5.3	5.4
	7.1	7.9	4.7	6.1
	6.3	7.9	5.5
	6.9		4.6
Total	33.9	29.5	25	15.9

	G	G^2
	7.2	51.84
	6.4	40.96
	7.1	50.41
	6.3	39.69
	6.9	47.61
	6.2	38.44
	7.5	56.25
	7.9	62.41
	7.9	62.41
	4.9	24.01
	5.3	28.09
	4.7	22.09
	5.5	30.25
	4.6	21.16
	4.4	19.36
	5.4	29.16
	6.1	37.21
Total	104.3	661.35

So we have Following table shows the calculations:

4. n3 5, п4 3. G 104.3 . G2-661.35

A)

(「GT 21.439

Now,

16.763 1n4 SS Between = 1n3 n2 n1

SSu, it hin-SST-SSBetween-21.439-16.763 = 4.676

B)

Since there are 4 different groups so we have k=4. Therefore degree of freedoms are:

between

difunt hin-Ņ-k = 17-4 = 13 wthan

dftotal - 13 +3- 16

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Now

SSbetueen5.5878 M Sbetueendfbetueen between

S Swithin = 0.3597 M Swithin = dfuit hin

C)

F test statistics is

MSbetween15.54 M Swithiun

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So p-value of the test is 0.0001. Since P-value is less than 0.05 so we can conclude that populations mean are different. We reject the claim that the quantity of dissolved oxygen does not vary from one location to another