Another type of painted ceramic vessel is called three-circle red-on-white (see reference in Problem 1). 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 5% level of signi­ficance?

In each problem, please provide the following information.

(a) What is the level of signifi­cance? State the null and alternate hypotheses.

(b) Find SS_TOT, SS_BET, and SSW and check that SS_TOT – SSB_ET + SS_W. Find d.f._BET, d.f._W, MS_BET, and MS_W. Find the value of the sample test statistic F (F ratio).

What are the degrees of freedom?

(c) Find (or estimate) the P-value of the sample test statistic.

(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis?

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

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

Site I 17 23 6 19 Site II 18 4 Site III 32 19 18 43 Site IV 13 19 14 34 12 15 25 16