There is an archaeological study area located in southwesternNew Mexico. Potsherds are broken pieces of prehistoric NativeAmerican clay vessels. One type of painted ceramic vessel is calledMimbres classic black-on-white. At three different sites,the number of such sherds was counted in local dwellingexcavations.

Site I	Site II	Site III
69	28	15
30	17	35
24	53	65
10	68	20
77		17
57		15
26

Shall we reject or not reject the claim that there is nodifference in population mean Mimbres classic black-on-white sherdcounts for the three sites? Use a 1% level of significance.

(a) What is the level of significance?


State the null and alternate hypotheses.

H₀: μ₁ =μ₂ = μ₃;H₁: Not all the means areequal.H₀: μ₁ =μ₂ = μ₃;H₁: At least two means areequal.     H₀:μ₁ = μ₂ =μ₃; H₁: Exactly two meansare equal.H₀: μ₁ =μ₂ = μ₃;H₁: All three means are different.

(b) Find SS_TOT,SS_BET, andSS_W and check thatSS_TOT =SS_BET +SS_W. (Round your answers to threedecimal places.)

SSTOT	=
SSBET	=
SSW	=

Find d.f._BET,d.f._W,MS_BET, andMS_W. (Round your answers forMS_BET, and MS_W totwo decimal places.)

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

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


What are the degrees of freedom?

d.f.N	=
d.f.D	=

(c) Find the P-value of the sample test statistic.

P-value > 0.1000.050 < P-value <0.100     0.025 < P-value <0.0500.010 < P-value < 0.0250.001 <P-value < 0.010P-value < 0.001

(d) Based on your answers in parts (a) to (c), will you reject orfail to reject the null hypothesis?

Since the P-value is greater than the level ofsignificance at α = 0.01, we do not rejectH₀.Since the P-value is less than orequal to the level of significance at α = 0.01, we rejectH₀.     Since theP-value is greater than the level of significance atα = 0.01, we reject H₀.Since theP-value is less than or equal to the level of significanceat α = 0.01, we do not reject H₀.

(e) Interpret your conclusion in the context of theapplication.

At the 1% level of significance there is insufficient evidenceto conclude that the means are not all equal.At the 1% level ofsignificance there is sufficient evidence to conclude that themeans are all equal.     At the 1% levelof significance there is insufficient evidence to conclude that themeans are all equal.At the 1% level of significance there issufficient evidence to conclude that the means are not allequal.

(f) Make a summary table for your ANOVA test. (Round your answersfor SS to three decimal places, your MS and F Ratio to twodecimal places, and your P-value to four decimalplaces.)

Source of Variation	Sum of Squares	Degrees of Freedom	MS	F Ratio	P-Value	Test Decision
Between groups					---Select--- p-value > 0.100 0.050 < p-value < 0.1000.025 < p-value < 0.050 0.010 < p-value < 0.025 0.001< p-value < 0.010 p-value < 0.001	---Select--- Reject H0. Do not reject H0.
Within groups
Total