Question

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 15 12 33 11 29 5 23 19 7 33 14 10 22 2 47 38 16 27 15 13 16 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: μ1 = μ2 = μ3 = μ4; H1: Exactly three means are equal. Ho: μ1 = μ2 = μ3 = μ4; H1: All four means are different. Ho: μ1 = μ2 = μ3 = μ4; H1: Exactly two means are equal. Ho: μ1 = μ2 = μ3 = μ4; H1: Not all the means are equal. Correct: Your answer is correct. (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. 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 (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 α = 0.05, we do not reject H0. Since the P-value is less than or equal to the level of significance at α = 0.05, we reject H0. Since the P-value is greater than the level of significance at α = 0.05, we reject H0. Since the P-value is less than or equal to the level of significance at α = 0.05, we do not reject H0. Correct: Your answer is correct. (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. Correct: Your answer is correct. (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

The data is considered as 6 values for site 1 and 5 for 2,3 and 4

A)Level of significance =0.05

Null and alternative hypothesis : Ho: μ1 = μ2 = μ3 = μ4; H1: Not all the means are equal.

B)SSTOT=2656.952

SSBET=338.652

SSW=2318.300

We get SSTOT = SSBET+ SSW

df BET=3

df W=17

MSBET=112.884

MSW=136.371

F= 0.828

Degrees of freedom =(3, 17)

C)P value is .497 > .1

D)The conclusion on Ho is Since the P-value is greater than the level of significance at α = 0.05, we do not reject H0.

E) Interpretation: At the 5% level of significance there is sufficient evidence to conclude that the means are all equal

F)ANOVA Table

Source	SS	df	MS	F	p value	Decision
Between	338.652	3	112.884	0.828	0.497	Accept
Within	2318.3	17	136.371
Total	2656.952	20