Some archaeologists theorize that ancient Egyptians interbred with several different immigrant populations over thousands of years. To see if there is any indication of changes in body structure that might have resulted, they measured 30 skulls of male Egyptians dated from 4000 B.C.E. and 30 others dated from 200 B.C.E. (Source: A. Thomson and R. Randall-Maciver, Ancient Races of the Thebaid, Oxford: Oxford University Press, 1905)
a) Are these data appropriate for inference? Explain.
b) Create a 95% confidence interval for the difference in mean skull breadth between these two eras.
c) Do these data provide evidence that the mean breadth of males' skulls changed over this period? Explain.
d) Perform Tukey's test for the difference. Do your conclusions of part c change?
e) Perform a rank sum test for the difference. Do your conclusions of part c change?