The data for deceased Major League Baseball (MLB) players in Table 7.2 were used [15] to investigate the research hypothesis that players with positive initials (like ACE) live longer, on average, than players with neutral initials (like GHR). For each birth year, the average age at death (AAD) was calculated for players with positive initials and for players with neutral initials (the control group). Calculate the difference between the positive and control AADs for each birth year and use these seven differences to test the null hypothesis that this population mean difference is equal to 0. (We implicitly assume that these data are a random sample.)

a. What is the two-sided P value?

b. Does the average value of the difference seem substantially different from 0?

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Birth Year Positive AAD Control AAD 1853 75.00 65.09 1876 77.00 62.12 1884 55.00 68.09 1885 73.00 69.39 1897 80.50 70.95 1903 80.00 71.60 1913 93.00 73.68