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
62 29 17
39 18 34
27 54 74
17 60 28
81 18
52 12
23

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: Exactly two means are equal.H0: μ1 = μ2 = μ3; H1: Not all the means are equal.    H0: μ1 = μ2 = μ3; H1: All three means are different.H0: μ1 = μ2 = μ3; 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.)

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 > 0.1000.050 < P-value < 0.100    0.025 < P-value < 0.0500.010 < P-value < 0.0250.001 < P-value < 0.010P-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 ---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

Homework Answers

Answer #1

(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)

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