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
69	26	15
39	16	31
29	50	72
10	63	29
80		10
57		17
29

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: ?₁ = ?₂ = ?₃; H₁: Exactly two means are equal.

H₀: ?₁ = ?₂ = ?₃; H₁: All three means are different.

H₀: ?₁ = ?₂ = ?₃; H₁: Not all the means are equal.

H₀: ?₁ = ?₂ = ?₃; H₁: At least 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?

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

(c) Find the P-value of the sample test statistic. (Round your answer to four decimal places.)


(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 ? = 0.01, we do not reject H₀.

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

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

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

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

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 FRatio 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						Reject H0/Do not reject H0.
Within groups
Total

Answer 1

(a)

Level of significance = 0.01

Null and Alternate hypotheses:

H0: Mean1 = Mean2 = Mean3 vs. H1: Not all the means are equal.

(b) & (f) ANOVA Table:

Source	SS	df	MS
Between-treatments	802.880	2	401.44	F = 0.73
Within-treatments	7666.179	14	547.58
Total	8469.059	16

The ANOVA Table gives the Sum of Squares, degrees of freedom, Mean SS, and value of F-statistic.

(c)

The p-value = 0.497974 = 0.4980 (rounded off to four decimal places)

(d)

Since the P value is greater than the level of significance at alpha = 0.01, we do not reject Ho.

(e)

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