There is an archaeological study area located in southwestern New Mexico. Potsherds are broken pieces of prehistoric Native American clay vessels. One type of painted ceramic vessel is calledMimbres classic black-on-white. At three different sites, the number of such sherds was counted in local dwelling excavations.

Site I Site II Site III

67 22 14

30 10 35

26 53 65

18 68 20

77 11

59 16

22

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.

(a) What is the level of significance?

State the null and alternate hypotheses.

(b) FindSS_TOT,SS_BET, andSS_Wand check thatSS_TOT=SS_BET+SS_W. (Round your answers to three decimal places.)

SS_TOT=

SS_BET=

SS_W=

Findd.f._BET,d.f._W,MS_BET, andMS_W. (Round your answers forMS_BET, andMS_Wto two decimal places.)

d.f._BET=

d.f._W=

MS_BET=

MS_W=

Find the value of the sampleFstatistic. (Round your answer to two decimal places.)

What are the degrees of freedom?

d.f._N=

d.f._D=