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 (67,35,28,17,82,50,26)

Site Il (28.18,54, 69)

Site III (13,35, 74, 24, 15, 11)

(b) Find SSTOT, SSBET, and SSW and check that SSTOT = SSBET + SSW. (Round your answers to three decimal places.)

SSTOT =

SSBET =

SSW =

Find d.f.BET, d.f.W, MSBET, and MSW. (Round your answers for MSBET, and MSW 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.

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.

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 Within groups Total

Answer 1

b)

SSTOT	8716.000
SSBET	812.202
SSW	7903.798
dfBET	2
dfW	14
MSBET	406.101
MSW	564.557
value of test statistic for factor A =				0.719
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 of Variation	SS	df	MS	F	P-value	decision
Between Groups	812.202	2	406.101	0.719	>0.10	fail to reject Ho
Within Groups	7903.798	14	564.557
Total	8716.000	16