Question

Where are the deer? Random samples of square-kilometer plots were taken in different ecological locations of a national park. The deer counts per square kilometer were recorded and are shown in the following table.

Mountain Brush	Sagebrush Grassland	Pinon Juniper
30	20	5
26	63	4
25	22	1
32	22	8

Shall we reject or accept the claim that there is no difference in the mean number of deer per square kilometer in these different ecological locations? Use a 5% level of significance.

(a) What is the level of significance?

(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 2 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)

c.

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
Within groups
Total

Answer 1

One factor ANOVA
	Mean	n	Std. Dev
	28.3	4	3.30	Mountain Brush
	31.8	4	20.85	Sagebrush Grassland
	4.5	4	2.89	Pinon Juniper
	21.5	12	16.84	Total
ANOVA table
Source	SS	df	MS	F	p-value
Treatment	1,758.500	2	879.25	5.808	.0240
Error	1,362.500	9	151.39
Total	3,121.000	11

ANSWERS:

(a) α = 0.05

(b) SSTOT = 3121.000, SSBET = 1758.500, SSW = 1362.500

3121.000 = 1758.500 + 1362.500

(c) dfBET = 20, dfW = 9, MSBET = 879.25, MSW = 151.39

(d) F = 5.808

(e) dFN = 2, dfD = 9

(f) Summary table shown above.

Decision: Since the p- value < 0.05, we reject Ho

Conclusion: There is sufficient evidence of a significant difference in the mean number of deer per square kilometer in these different ecological locations.