here is an archaeological study area located in southwestern New Mexico. Potsher

Question

here 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.

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.

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

Find d.f.BET, d.f.W, MSBET, and MSW. (Round your answers for MSBET, and MSW to two decimal places.)

Find the value of the sample F statistic. (Round your answer to two decimal places.)


What are the degrees of freedom?

(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?

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

(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.)

Site I Site II Site III 62 29 18 34 14 36 22 52 72 13 65 28 83 15 57 19 22

Explanation / Answer

All answers are derived from table below using excel

a) level of significance = 0.01

option D) H0: 1 = 2 = 3; H1: Not all the means are equal. is correct

b)

c)

d) option A) Since the P value is greater than the level of significance at = 0.01, we do not reject H0. is correct

e)

option A) is correct

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

f) table already included at top

Decision fail to reject the null

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Anova: Single Factor SUMMARY Groups Count Sum Average Variance Site I 7 293 41.85714286 668.4762 Site II 4 160 40 522 Site III 6 188 31.33333333 456.6667 ANOVA Source of Variation SS df MS F P-value F crit Between Groups 385.3389356 2 192.6694678 0.343169 0.7153222 3.738891832 Within Groups 7860.190476 14 561.4421769 Total 8245.529412 16

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