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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 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.

Ho: ?1 = ?2 = ?3 = ?4; H1: Exactly three means are equal.

Ho: ?1 = ?2 = ?3 = ?4; H1: All four means are different.    

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

Ho: ?1 = ?2 = ?3 = ?4; H1: Exactly two means are equal.



(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. (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

Homework Answers

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.

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