Question

Another type of painted ceramic vessel is called three-circle red-on-white ( Mimbres Mogollon Archaeology). At four different sites in an archaeological region, the number of such sherds was counted in local dwelling excavations.

Site I	Site II	Site III	Site IV
19	15	38	13
22	8	15	17
5	30	10	16
22	8	47	37
10	24		19
	12		18

Shall we reject or not reject the claim that there is no difference in the population mean three-circle red-on-white sherd counts for the four sites? 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 = μ₄; H₁: Not all the means are equal.

H_o: μ₁ = μ₂ = μ₃ = μ₄; H₁: Exactly two means are equal.    

H_o: μ₁ = μ₂ = μ₃ = μ₄; H₁: Exactly three means are equal.

H_o: μ₁ = μ₂ = μ₃ = μ₄; H₁: All four 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 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)

(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 following--- Do not reject H0. -- Reject H0.
Within groups
Total

Answer 1

Applying one way ANOVA: (use excel: data: data analysis: one way ANOVA: select Array):

a)level of significance=0.05

H_o: μ₁ = μ₂ = μ₃ = μ₄; H₁: Not all the means are equal.

b)

SSTOT	2362.286
SSBET	399.252
SSW	1963.033

dfBET	3
dfW	17
MSBET	133.084
MSW	115.473

value of test statistic for factor A =

1.153

df(numerator) =		3
df(Denominator) =		17

c)

p value = 0.3566

d) fail to reject the null hypothesis

e) can not conclude that means are different

f)

Source	SS	df	MS	F	P value
Between	399.252	3	133.084	1.153	0.3566
Within	1963.033	17	115.473
Total	2362.286	20