Aresearcher wished to compare the effect of two stepping heights (low and high) on heart rate in a step‑aerobics workout. a collection of 50 adult volunteers was randomly divided into two groups of 25 subjects each. group 1 did a standard step‑aerobics workout at the low height. the mean heart rate at the end of the workout for the subjects in group 1 was ¯1=90 beats per minute with a standard deviation of =9 beats per minute. group 2 did the same workout but at the high step height. the mean heart rate at the end of the workout for the subjects in group 2 was ¯2=95.08 beats per minute with a standard deviation of =12 beats per minute. assume that the two groups are independent and that the data are approximately normal. let and represent the mean heart rates we would observe for the entire population represented by the volunteers, if all members of this population did the workout using the low or high step height, respectively. suppose the researcher wished to test the hypotheses : = and : < . using the conservative value for the degrees of freedom, the ‑value for the test is: between 0.1 and 0.05. between 0.05 and 0.01. larger than 0.1.