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?

Maximum Skull Breadth (mm) 4000 ... 200 ... 4000 ... 131 125 131 119 136 138 139 125 131 134 129 134 126 132 141 131 135 132 139 132 126 135 134 128 130 138 128 127 131 124 141 141 135 133 131 140 139 140 138 132 134 135 133 136 134 200 ... 131 129 136 131 139 144 141 130 133 138 131 136 132 135 141