There is an archaeological study area located in southwestern New Mexico. Potshe

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.

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 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?

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.)

Site I Site II Site III 69 26 15 39 16 31 29 50 72 10 63 29 80 10 57 17 29

Explanation / Answer

(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:

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.

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

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