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	24	10
32	56	7
22	14	6
34	17	7

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?

State the null and alternate hypotheses.(from the following)
H_o: μ₁ = μ₂ = μ₃; H₁: At least two means are equal.

H_o: μ₁ = μ₂ = μ₃; H₁: Not all the means are equal.    

H_o: μ₁ = μ₂ = μ₃; H₁: Exactly two means are equal.

H_o: μ₁ = μ₂ = μ₃; H₁: All three means are different.

(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) Find 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.

Source of Variation	Sum of Squares	Degrees of Freedom	MS	F Ratio	P Value	Test Decision
Between groups					---Select from the following--- 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 from the following--- Do not reject H0. -- Reject H0.
Within groups
Total

Answer 1