The Etruscans. Anthropologists are still trying to unravel the mystery of the origins of the Etruscan empire, a highly advanced Italic civilization formed around the eighth century B.C. in central Italy. Were they native to the Italian peninsula or, as many aspects of their civilization suggest, did they migrate from the East by land or sea? The maximum head breadth, in millimeters, of 70 modern Italian male skulls and that of 84 preserved Etruscan male skulls were analyzed to help researchers decide whether the Etruscans were native to Italy. The resulting data can be found on the WeissStats site.

[SOURCE: N. Barnicot and D. Brothwell, “The Evaluation of Metrical Data in the Comparison of Ancient and Modern Bones.” In Medical Biology and Etruscan Origins, G. E. W. Wolstenholme and C. M. O’Connor, eds., Little, Brown & Co., 1959] Use the technology of your choice to solve parts (a)–(c).

a. Perform a two-standard-deviations F-test at the 5% significance level to decide whether the data provide sufficient evidence to conclude that variations in skull measurements differ between the two populations.

b. Use the two-standard-deviations F-interval procedure to determine a 95% confidence interval for the ratio of the standard deviations of skull measurements of the two populations.

c. Obtain a normal probability plot for each sample.

d. In light of your plots in part (c), does conducting the inferences you did in parts

(a) and

(b) seem reasonable? Explain your answer.