Farren et al. (2004) compared the toughness of human fingernails along a transverse dimension (side to side) with toughness along a longitudinal direction, with 15 measurements of each. the toughness of fingernails, along a transverse direction average 3.3 kg/m2, with a standard deviation of 0.95, while the mean toughness along the longitudinal direction was 6.2 kj/m2, with a standard deviation of 1.48 kj/m2.
test for a significant difference in the toughness of these fingernails along the two dimensions. assume that the data are from two independent samples of 15 people.
as it turns out, all of the fingernails in this study came from the same volunteer. how does this alter you conclusion from part (a)? briefly, what steps would you take to design this study properly?