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
65	21	17
30	19	35
23	53	71
17	68	24
76		12
52		17
21

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.

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

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

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

H₀: 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. (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?

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

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

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

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

Since the P-value is greater than the level of significance at α = 0.01, we do not reject H₀.

Since the P-value is less than or equal to the level of significance at α = 0.01, we reject H₀.    

Since the P-value is greater than the level of significance at α = 0.01, we reject H₀.

Since the P-value is less than or equal to the level of significance at α = 0.01, we do not reject H₀.

(e) Interpret your conclusion in the context of the application. Select one

At the 1% level of significance there is insufficient evidence to conclude that the means are not all equal.

At the 1% level of significance there is sufficient evidence to conclude that the means are all equal.    

At the 1% level of significance there is insufficient evidence to conclude that the means are all equal.

At the 1% level of significance there is sufficient evidence to conclude that the means are not all equal.

(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--- 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--- 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)the level of significance =0.01

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

b)

SSTOT	7978.235
SSBET	480.438
SSW	7497.798

dfBET	2
dfW	14
MSBET	240.22
MSW	535.56

value of test statistic for factor A =

0.45

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

c)

P-value > 0.100

d)

Since the P-value is greater than the level of significance at α = 0.01, we do not reject H₀.

e)

At the 1% level of significance there is insufficient evidence to conclude that the means are not all equal.

f)

Source	SS	df	MS	F	P value
Between	480.438	2	240.22	0.45	0.6474
Within	7497.798	14	535.56		do not reject Ho
Total	7978.235	16