Question

Another type of painted ceramic vessel is called three-circle red-on-white ( Mimbres Mogollon Archaeology). At four...

Another type of painted ceramic vessel is called three-circle red-on-white ( Mimbres Mogollon Archaeology). At four different sites in an archaeological region, the number of such sherds was counted in local dwelling excavations.

Site I Site II Site III Site IV
19 15 38 13
22 8 15 17
5 30 10 16
22 8 47 37
10 24 19
12 18

Shall we reject or not reject the claim that there is no difference in the population mean three-circle red-on-white sherd counts for the four sites? Use a 5% level of significance.

(a) What is the level of significance?

State the null and alternate hypotheses (from the following).

Ho: μ1 = μ2 = μ3 = μ4; H1: Not all the means are equal.

Ho: μ1 = μ2 = μ3 = μ4; H1: Exactly two means are equal.    

Ho: μ1 = μ2 = μ3 = μ4; H1: Exactly three means are equal.

Ho: μ1 = μ2 = μ3 = μ4; H1: All four means are different.

(b) Find SSTOT, SSBET, and SSW and check that SSTOT = SSBET + SSW. (Use 3 decimal places.)

SSTOT =
SSBET =
SSW =


Find d.f.BET, d.f.W, MSBET, and MSW. (Use 3 decimal places for MSBET, and MSW.)

dfBET =
dfW =
MSBET =
MSW =


Find the value of the sample F statistic. (Use 3 decimal places.)


What are the degrees of freedom?
(numerator)
(denominator)

(c) Find the P-value of the sample test statistic.
(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.

Source of
Variation
Sum of
Squares
Degrees of
Freedom
MS F
Ratio
P Value Test
Decision
Between groups ---Select from the following--- 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 from following--- Do not reject H0. -- Reject H0.
Within groups
Total

Homework Answers

Answer #1
Applying one way ANOVA: (use excel: data: data analysis: one way ANOVA: select Array):

a)level of significance=0.05

Ho: μ1 = μ2 = μ3 = μ4; H1: Not all the means are equal.

b)

SSTOT 2362.286
SSBET 399.252
SSW 1963.033
dfBET 3
dfW 17
MSBET 133.084
MSW 115.473
value of test statistic for factor A = 1.153
df(numerator) = 3
df(Denominator) = 17

c)

p value = 0.3566

d) fail to reject the null hypothesis

e) can not conclude that means are different

f)

Source SS df MS F P value
Between 399.252 3 133.084 1.153 0.3566
Within 1963.033 17 115.473
Total 2362.286 20
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