Question

In: Statistics and Probability

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
17 11 31 10
28 8 17 16
5 31 13 11
17 9 47 32
12 22 12
18 19

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

SSTOT =
SSBET =
SSW =

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

dfBET =
dfW =
MSBET =
MSW =

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

d) What are the degrees of freedom?

(numerator) =

(denominator) =

e) Find the P-value of the sample test statistic.

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

(f) Make a summary table for your ANOVA test.

Source of
Variation

Sum of
Squares

Degrees of
Freedom

MS

F
Ratio

Between groups

Within groups  

Total

Solutions

Expert Solution

Here we have data:

Site I Site II Site III Site IV
17 11 31 10
28 8 17 16
5 31 13 11
17 9 47 32
12 22 12
18 19

We are using Excel for calculation:

f)

Anova: Single Factor
SUMMARY
Groups Count Sum Average Variance
Column 1 5 79 15.8 70.7
Column 2 6 99 16.5 80.3
Column 3 4 108 27 237.3333
Column 4 6 100 16.66667 67.86667
ANOVA
Source of Variation SS df MS F P-value F crit
Between Groups 369.319 3 123.106 1.206 0.3377 3.197
Within Groups 1735.633 17 102.096
Total 2104.952 20

a)

SSTOT = 2104.952

SSBET = 369.319

SSW = 1735.633

B)

DFBET = 3

DFW = 17

MSBET = 123.106

MSW = 102.096

c)

F- statistics = 1.206

d)

Numerator = 3

Denominator = 17

e) P-value of the test statistics = 0.3377

Correct option "A"

P-value > 0.100


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