An athletic coach wishes to test whether his proposed weight training program improves the running performance of his athletes. He selects 12 athletes at random and has them run a 400 meters distance and records their times (in seconds). Then the athletes undergo his training program, and at the end of it, their time for running the 400 meters distance is taken again. Denote by μ_before and μ_after the mean time (in seconds) for running the 400 meters distance before and after the weight training program. Denote by d_i the time difference after and before the program for athlete i, e.g., d_1 = 50.6 − 51.0 = −0.4. A one-sample t-test is conducted.