Question

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

Site I	Site II	Site III	Site IV
14	14	39	11
28	8	17	20
5	37	10	15
22	2	49	37
12	25		16
	17		10

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 10% level of significance.

(a) What is the level of significance?

State the null and alternate hypotheses.

H_o: ?₁ = ?₂ = ?₃ = ?₄; H₁: Exactly two means are equal.H_o: ?₁ = ?₂ = ?₃ = ?₄; H₁: Exactly three means are equal.    H_o: ?₁ = ?₂ = ?₃ = ?₄; H₁: All four means are different.H_o: ?₁ = ?₂ = ?₃ = ?₄; H₁: Not all the means are equal.

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

SSTOT	=
SSBET	=
SSW	=

Find d.f._BET, d.f._W, MS_BET, and MS_W. (Use 3 decimal places for MS_BET, and MS_W.)

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. (Use 4 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 ? = 0.1, we do not reject H₀.Since the P value is less than or equal to the level of significance at ? = 0.1, we reject H₀.    Since the P value is greater than the level of significance at ? = 0.1, we reject H₀.Since the P value is less than or equal to the level of significance at ? = 0.1, we do not reject H₀.

(e) Interpret your conclusion in the context of the application.

At the 10% level of significance there is insufficient evidence to conclude that the means are not all equal.At the 10% level of significance there is sufficient evidence to conclude that the means are all equal.    At the 10% level of significance there is insufficient evidence to conclude that the means are all equal.At the 10% 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.

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

Answer 1

a)

level of significance=0.1

Ho: ?1 = ?2 = ?3 = ?4; H1: Not all the means are equal.

b)

SSTOT =2534.755

SSBET =430.372

SSW =2104.383

dfBET =3

dfW=17

MSBET =143.457

MSW =123.787

value of the sample F statistic =MSBET/MSW =1.159

numerator df =3

denominator df =17

c)

p vlaue =0.3543

d)

Since the P value is greater than the level of significance at ? = 0.1, we do not reject H0

e)At the 10% level of significance there is insufficient evidence to conclude that the means are not all equal

f)

Source of variation		SS	df	MS	F	p vlaue
treatments		430.372	3.00	143.457	1.159	0.3543
error		2104.383	17.00	123.787
total		2534.755	20.00

do not reject Ho