Another type of painted ceramic vessel is called three-circle red-on-white ( Mim

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.

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 1% level of significance.

(a) What is the level of significance?

State the null and alternate hypotheses: Ho: 1 = 2 = 3 = 4; H1: Not all the means are equal.  

(b) Find SSTOT, SSBET, and SSW and check that SSTOT = SSBET + SSW. (Use 3 decimal places.)

Find d.f.BET, d.f.W, MSBET, and MSW. (Use 3 decimal places for MSBET, and MSW.)

(c) Find the value of the sample F statistic. (Use 3 decimal places.)
____________

(d) What are the degrees of freedom?
(numerator)____________
(denominator)____________

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

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 = 0.01, we do not reject H0.

Interpret your conclusion in the context of the application: At the 1% level of significance there is insufficient evidence to conclude that the means are not all equal.

(f) Make a summary table for your ANOVA test.

Site I Site II Site III Site IV 19 19 33 13 27 4 17 18 6 37 14 13 21 6 46 30 19 26 17 17 19 Find SS SSBET, and SSw and check that SSTOT SSBET SSW. (Use 3 decimal places TOT, SS TOT SS BET ssw Find d., f. BET, d.f, W, MS and MSW. (Use 3 decimal places for MS and W. BET, dfi BET dfl MSBET MS Make a summary table for your ANOVA test. Source of Sum of Degrees of Test P Value MS Variation Freedom Ratio Decision Squares Select Between groups Select Within groups Do not reject H0. Total Reject HO.

Explanation / Answer

The R code is:

data <- c(19,27,6,21,19,19,4,37,6,26,17,33,17,14,46,13,18,13,30,17,19)
sites <-c(rep("site 1",5), rep("site 2",6), rep("site 3", 4), rep("site 4",6))
summary(aov(data~sites))

The output is:

Df Sum Sq Mean Sq F value Pr(>F)
sites 3 274.6 91.53 0.835 0.493
Residuals 17 1862.4 109.55

Since p-value is high, the null hypothesis is not rejected.

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