Question

# There is an archaeological study area located in southwestern New Mexico. Potsherds are broken pieces of...

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

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

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