Have you ever noticed that, when you tear a fingernail, it tendsto tear to the side and not down into the finger? (Actually, thelatter doesn’t bear too much thinking about.). Why might this beso? One possibility is that fingernails are tougher in onedirection than another. A study of the toughness of humanfingernails compared the toughness of nails along a transversedimension (side to side) compared with a longitudinal direction,with 15 measurements of each (Farren et al., 2004). The toughnessof fingernails along a transerve direction averaged 3.3 kJ/m2, witha standard deviation of 0.95, while the mean toughness along thelongitudinal direction was 6.2 kJ/m2, with a standard deviation of1.48 kJ/m2. a) Test for a significant difference in the toughnessof these fingernails along two dimensions. b) As it turns out, allof the fingernails in this study came from the same volunteer.Discuss what the conclusion in part (a) means. What would berequired to describe the fingernail toughness of all humans?
