Elevated energy consumption during exercise continues after the workout ends. Because calories burned after exercise contribute to weight loss and have other consequences, it is important to understand this process. The paper “Effect of Weight Training Exercise and Treadmill Exercise on Post-Exercise Oxygen Consumption” (Medicine and Science in Sports and Exercise, 1998: 518–522) reported the accompanying data from a study in which oxygen consumption (liters) was measured continuously for 30 minutes for each of 15 subjects both after a weight training exercise and after a treadmill exercise. a. Construct a comparative boxplot of the weight and treadmill observations, and comment on what you see. b. Because the data is in the form of (x, y) pairs, with x and y measurements on the same variable under two different conditions, it is natural to focus on the differences within pairs: d1 = x1-y1,….,dn = xn – yn . Construct a boxplot of the sample differences. What does it suggest?
Answer: Step1: Given that, reported the accompanying data from a study in which oxygen consumption (liters) was measured continuously for 30 minutes for each of 15 subjects both after a weight training exercise and after a treadmill exercise. The data is given by Subject Weight Treadmill (x) (y) 1 14.6 11.3 2 14.4 5.3 3 19.5 9.1 4 24.3 15.2 5 16.3 10.1 6 22.1 19.6 7 23 20.8 8 18.7 10.3 9 19 10.3 10 17 2.6 11 19.1 16.6 12 19.6 22.4 13 23.2 23.6 14 18.5 12.6 15 15.9 4.4 a). To construct a comparative boxplot of the weight and treadmill observations. For weight for treadmill th th Upper fourth = ( 154+ 1× 3) Upper fourth = ( 15 4 1× 3) th th = 12 = 12 = 19.6 = 22.4 15+1 th 15+1 th Lower fourth = ( 4 ) Lower fourth = ( 4 ) = 4th = 4th = 24.3 = 15.2 Fourth spread(sp) = U - L Fourth spread(sp) = U - L = 22.4 - 15.2 = 19.6 - 24.3 = 7.2 = - 4.7 Conclusion: there is a significant difference in the variability of two samples. Here weight is the much higher oxygen consumption than the treadmill, with the median consumption 11 and 20. b). Because the data is in the form of (x, y) pairs, with x and y measurements on the same variable under two different conditions. Differences within pairs d =ix i ( ieight - treadmill). That is, d i 3.3 9.1 10.4 9.1 6.2 2.5 2.2 8.4 8.7 14.4 2.5 -2.8 -0.4 5.9 11.5 Arrange the data in ascending order. -2.8 -0.4 2.2 2.5 2.5 3.3 5.9 6.2 8.4 8.7 9.1 9.1 10.4 11.5 14.4 Median = 6.2 ( if n is odd, the median is the middle value.) Consider lower half of the data. Select the data before median. -2.8 -0.4 2.2 2.5 2.5 3.3 5.9 Therefore, lower fourth = 2.5 ( here n is odd, so lower fourth is the middle value) Consider upper half data that. Select the data after the median. 8.4 8.7 9.1 9.1 10.4 11.5 14.4 Therefore, upper fourth = 9.1 ( here n is odd, so upper fourth is the middle value) Fourth spread = upper fourth - lower fourth = 9.1 - 2.5 = 6.6 A boxplot of the sample differences. Conclusion: the most of the differences are positive. It’s suggests weight training produced higher oxygen consumption for most subjects than the treadmill consumption with the median difference is about 6 liters.
