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 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 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. 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

 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 7978.23 SSBET 480.438 SSW 7497.8
 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