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	17	39	10
29	3	17	22
4	35	12	15
20	6	49	31
11	24		13
	18		17

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.

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.

H_o: ?₁ = ?₂ = ?₃ = ?₄; H₁: Exactly two 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 ? = 0.05, we do not reject H₀.

Since the P value is less than or equal to the level of significance at ? = 0.05, we reject H₀.   

Since the P value is greater than the level of significance at ? = 0.05, we reject H₀.

Since the P value is less than or equal to the level of significance at ? = 0.05, we do not reject H₀.

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

At the 5% level of significance there is insufficient evidence to conclude that the means are not all equal.

At the 5% level of significance there is sufficient evidence to conclude that the means are all equal.  

  At the 5% level of significance there is insufficient evidence to conclude that the means are all equal.

At the 5% 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						Do not reject H0/Reject H0.
Within groups
Total

Answer 1

a) The null and alternate hypotheses are

against H₁ : Not all the means are equal.

b) SSTOT = 2766.7, SSBET = 2264.8, SSW = 501.9

dfBET = 3, dfW = 17

MSBET = 167.3, MSW = 133.2

The value of the sample F statistic = 1.26

The degrees of freedom = (3, 17)

c) The P-value of the sample test statistic = 0.321

d) Since the P value is greater than the level of significance at = 0.05, we do not reject H₀.

e) At the 5% level of significance there is insufficient evidence to conclude that the means are not all equal.