In a study comparing age of death for left-and right-handed baseball players, Coren and Halpern (1991, p. 93) provided the following information: “Mean age of death for strong right-handers was 64.64 years (SD = 15.5, n = 1472); mean age of death for strong left-handers [was] 63.97 years (SD = 15.4, n = 236).” The term “strong handers” applies to baseball players who both threw and batted with the same hand. The data were actually taken from entries in The Baseball Encyclopedia (6th ed., New York: Macmillan, 1985), but, for the purposes of this exercise, pretend that the data were from a sample drawn from a larger population.
a. Compute an approximate 95% confidence interval for the mean age of death for the population of strong right-handers from which this sample was drawn.
b. Repeat part (a) for the strong left-handers.
c. Compare the results from parts (a) and (b) in two ways. First, explain why one confidence interval is substantially wider than the other. Second, explain whether you would conclude that there is a difference in the mean ages of death for left- and right-handers on the basis of these results.
d. Compute an approximate 95% confidence interval for the difference in mean ages of death for the strong right-and left-handers. Interpret the result.