Question

There is an archaeological study area located in southwestern New Mexico. Potsherds are broken pieces of prehistoric Native American clay vessels. One type of painted ceramic vessel is called Mimbres classic black-on-white. At three different sites, the number of such sherds was counted in local dwelling excavations.

Site I	Site II	Site III
64	24	18
33	14	30
22	50	73
17	61	29
82		14
56		16
26

Shall we reject or not reject the claim that there is no difference in population mean Mimbres classic black-on-white sherd counts for the three sites? Use a 1% level of significance.

(a) What is the level of significance?

State the null and alternate hypotheses. (from the following)

H₀: μ₁ = μ₂ = μ₃; H₁: All three means are different.

H₀: μ₁ = μ₂ = μ₃; H₁: At least two means are equal.    

H₀: μ₁ = μ₂ = μ₃; H₁: Not all the means are equal.

H₀: μ₁ = μ₂ = μ₃; H₁: Exactly two means are equal.

(b) Find SS_TOT, SS_BET, and SS_W and check that SS_TOT = SS_BET + SS_W. (Round your answers to three decimal places.)

SSTOT	=
SSBET	=
SSW	=

Find d.f._BET, d.f._W, MS_BET, and MS_W. (Round your answers for MS_BET, and MS_W to two decimal places.)

d.f.BET	=
d.f.W	=
MSBET	=
MSW	=

Find the value of the sample F statistic. (Round your answer to two decimal places.)

What are the degrees of freedom?

(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. (Round your answers for SS to three decimal places, your MS and F Ratio to two decimal places, and your P-value to four decimal places.)

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

Answer 1

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

a)

H₀: μ₁ = μ₂ = μ₃; H₁: Not all the means are equal.

SSTOT	8060.000
SSBET	534.393
SSW	7525.607

dfBET	2
dfW	14
MSBET	267.20
MSW	537.54

value of test statistic for factor A =

0.50

df(numerator) =		2
df(Denominator) =		14

c) p value =0.6187

d)  fail to reject the null hypothesis

e) we can not conclude that population means are not equal

f)

Source	SS	df	MS	F	P value
Between	534.393	2	267.20	0.50	0.6187
Within	7525.607	14	537.54
Total	8060.000	16