11.36 The authors of the paper “Ultrasound Techniques Applied to Body Fat Measurement in Male and Female Athletes” (Journal of Athletic Training [2009]: 142–147)

compared two different methods for measuring body fat percentage. One method uses ultrasound, and the other method uses X-ray technology. Body fat percentages using each of these methods for 16 athletes

(a subset of the data given in a graph that appeared in the paper) are given in the accompanying table. For purposes of this exercise, you can assume that the 16 athletes who participated in this study are representative of the population of athletes. Use these data to estimate the difference in mean body fat percentage measurement for the two methods. Use a confidence level of 95% and interpret the interval in context.

Athlete X-ray Ultrasound 1 5.00 4.75 2 7.00 3.75 3 9.25 9.00 4 12.00 11.75 5 17.25 17.00 6 29.50 27.50 7 5.50 6.50 8 6.00 6.75 9 8.00 8.75 10 8.50 9.50 11 9.25 9.50 12 11.00 12.00 13 12.00 12.25 14 14.00 15.50 15 17.00 18.00 16 18.00 18.25