Question

The authors of a paper 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.

Athlete	X-ray	Ultrasound
1	5.00	4.50
2	9.00	5.75
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	14.50	15.50
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

Use these data to estimate the difference in mean body fat percentage measurement for the two methods. Use a confidence level of 95%. (Use ?_X-ray ? ?_ultrasound. Round your answers to three decimal places.)
to  %

Interpret the interval in context.

We are 95% confident that the true mean body fat percentage measurement for X-rays is between these two values.We are 95% confident that the true difference in mean body fat percentage measurement for the two methods is between these two values.    There is a 95% chance that the true mean body fat percentage measurement for X-rays is directly in the middle of these two values.We are 95% confident that the true mean body fat percentage measurement for ultrasounds is between these two values.There is a 95% chance that the true difference in mean body fat percentage measurement for the two methods is directly in the middle of these two values.

Answer 1

The statistical software output for this problem is:

Paired T confidence interval:
?_D = ?₁ - ?₂ : Mean of the difference between X-ray and Ultrasound
95% confidence interval results:

Difference	Mean	Std. Err.	DF	L. Limit	U. Limit
X-ray - Ultrasound	-0.078125	0.30594692	15	-0.73023541	0.57398541

Hence,

95% confidence interval: -0.730% to 0.574%

We are 95% confident that the true difference in mean body fat percentage measurement for the two methods is between these two values.