Shaft graves in ancient Greece. Refer to the American Journal of Archaeology (Jan. 2014) study of sword shaft graves in ancient Greece, Exercise 2.37 (p. 78). The number of sword shafts buried at each of 13 recently discovered grave sites is reproduced in the following table. Let s represent the standard deviation of the number of sword shafts for the population of all shaft graves in ancient Greece. Consider the test H0: s = 3 versus Ha: s 6 3, using a = .05.

1 2 3 1 5 6 2 4 1 2 4 2 9 Source: Harrell, K. “The fallen and their swords: A new explanation for LO9 the rise of the shaft graves.” American Journal of Archaeology, Vol. 118, No. 1, Jan. 2014 (Figure 1).

a. Use statistical software to find the sample standard deviation, s.

b. Calculate the test statistic.

c. Use statistical software to find the p-value of the test.

Interpret the result.

d. Assume the sample grave with 9 sword shafts was discovered to be an outlying observation by the researchers, i.e., one from a different population.

Remove the data point from the sample and repeat parts a–c. What conclusions can you now draw?