Chapter 10.5, Problem 1P

In each problem, assume that the distributions are normal and have approximately the same population standard deviation.

In each problem, please provide the following information.

1. (a) What is the level of significance? State the null and alternate hypotheses.
2. (b) Find SS_TOT, SS_BET, and SS_W and check that SS_TOT = SS_BET + 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?
3. (c) Find (or estimate) the P-value of the sample test statistic.
4. (d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis?
5. (e) Interpret your conclusion in the context of the application.
6. (f) Make a summary table for your ANOVA test.

Archaeology: Ceramics Wind Mountain is an archaeological study area located in southwestern New Mexico. Pot sherds are broken pieces of prehistoric Native American clay vessels. One type of painted ceramic vessel is called Mimbres classic black-on-white. At three different sites, the number of such sherds was counted in local dwelling excavations (Source: Based on information from Mimbres Mogollon Archaeology by A. I. Woosley and A. J. McIntyre, University of New Mexico Press).

Shall we reject or not reject the claim that there is no difference in population mean Mimbres classic black-on-white sherd counts for the three sites? Use a 1% level of significance.