Blood coagulates as a result of a complex sequence of chemical reactions. The protein thrombin triggers the clotting of blood under the influence of another protein called prothrombin. One measure of a person's blood clotting ability is expressed in prothrombin time, which is defined to be the interval between the initiation of the thrombin-prothrombin reaction and the formation of the clot. One study (209) looked at the effect of aspirin on prothrombin time. The preceding table gives, for each of twelve subjects, the prothrombin time (in seconds) before and three hours after taking two aspirin tablets (650 mg). Test the hypothesis that aspirin influences prothrombin times. Perform the test at both the α = 0.05 and α = 0.01 levels.

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Subject Before Aspirin, x After Aspirin, y 12.3 12.0 12.0 13.0 13.0 12.5 11.3 11.8 11.5 11.0 11.0 11.3 12.0 12.3 12.5 12.0 13.0 12.5 10.3 11.3 11.5 11.5 11.0 11.5 7 10 12