Excavating ancient pottery. Refer to the Chance (Fall 2000) study of ancient Greek pottery, presented in Exercise 2.186 (p. 134). Recall that 837 pottery pieces were uncovered at the excavation site. The table describing the types of pottery found is reproduced here.

Pot Category Number Found Burnished 133 Monochrome 460 Painted 183 Other 61 Total 837 Based on Berg, I., and Bliedon, S. “The pots of Phyiakopi:

Applying statistical techniques to archaeology.” Chance, Vol. 13, No. 4, Fall 2000.

a. Describe the qualitative variable of interest in the study. Give the levels (categories) associated with the variable.

b. Assume that the four types of pottery occur with equal probability at the excavation site. What are the values of p1, p2, p3, and p4, the probabilities associated with the four pottery types?

c. Give the null and alternative hypotheses for testing whether one type of pottery is more likely to occur at the site than any of the other types.

d. Find the test statistic for testing the hypotheses stated in part c.

e. Find and interpret the p-value of the test. State the conclusion in the words of the problem if you use a = .10.

Transcribed Image Text:

Model The FREQ Procedure Table of Model by Claim Claim Injury No Injury Total Conventional Frequency 5364 Total Expected 5340.7 Hybrid Frequency 137 Expected 160.33 Frequency 5501 44791 44768 50132 1368 1505 1344.7 46136 51637 Statistics for Table of Model by Claim Statistic DF Value Prob Chi-Square 1 3.9139 0.0479 Likelihood Ratio Chi-Square 1 4.0893 0.0432 1 3.7480 0.0529 Continuity Adj. Chi-Square Mantel-Haenszel Chi-Square 1 3.9138 0.0479 Phi Coefficient Contingency Coefficient Cramer's V 0.0087 0.0087 0.0087 Pearson Chi-Square Test Chi-Square DF 3.9139 1 Asymptotic Pr> ChiSq 0.0479 Exact Pr >= Chi Sq 0.0510