Question

Wind Mountain 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
61	26	13
34	10	31
28	55	65
18	63	22
78		15
50		19
26

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 10% level of significance.

(b) Find SS_TOT, SS_BET, and SS_W and check that SS_TOT = SS_BET + SS_W. (Use 3 decimal places.)

SS_TOT

SSBET

SS_W

Find d.f._BET, d.f._W, MS_BET, and MS_W. (Use 2 decimal places for MS_BET, and MS_W.)

df_BET

df_W

MSBET

MSW

Find the value of the sample F statistic. (Use 2 decimal places.)

What are the degrees of freedom?

（ numerator）

  (denominator)
(c) Find the P-value of the sample test statistic. (Use 4 decimal places.)

(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						.
Within groups
Total

Answer 1

A ) level of significance is 10% ( 0.10)

Hypothesis

No all means are equal

B) Enter data in excel sheet like this

Go to DATA ribbon. Choose ANOVA : One factor from data Analysis menu.

Output from Excel( ANOVA Table )

SSTOT = 726.765

SSBET = 722.4076

SSW = 6541.357

There are k = 3 treatment and N = 17 total observations therefore,

dfBET = ( k - 1 ) = ( 3 - 1) = 2

dfW = ( N - k ) = ( 17 - 3 ) = 14

MSBET = SBET / dfBET = 722.4076 / 2 = 361.2038

MSW = SW / dfW = 6541.357 / 14 = 467.2398

F = MSBET / MSW = 0.770359

The degree of freedom for F statistics is

dfN = 2

dfD = 14

C ) The p value for the test can be obtained using Excel functon FDIST(F,dfN,dfD) as :

p value = FDIST(0.773059,2,14) = 0.480333

Since p value is greter than level of significance at 0.10 , We do not reject null hypothesis

At 10% level of significance there is sufficient evidence that the means are equal