Consider the NHANES III population data provided in Table 15.2 and discussed in Example 15.4. Collect an unbalanced RSS (see the "Unbalanced Ranked Set Sampling" discussion in this section) of size n = 96 from this population using set size k = 5 and buttocks circumference as the auxiliary variable for the ranking process by obtaining the BMI value for the subject with the median buttocks circumference in each of the 96 sets of size 5. Thus, the collected BMI data will be of the form X[3]j = jth set sample median for each of the sets j = 1, 2, ... , 96. Use these data to estimate the average BMI for the entire NHANES III population. Compare this estimate with the four estimates of the same quantity using the balanced RSSs of 96 NHANES III subjects each obtained in Problems 14-17 and the estimate from the SRS of size 96 obtained in Problem 26. How do these six estimates compare with the actual average BMI for the entire population?
Example 15.4
The NHANES III survey, 1988-1994, was conducted by the National Center for Health Statistics, Centers for Disease Control and Prevention. This survey was designed to obtain nationally representative information on the health and nutritional status of the population of the United States. The data set contains information for 33,994 persons aged 2 months and older who participated in the survey. Specifically, it contains various body measurements and information on other health-related variables for the respondents. The survey used a complex, multistage cluster sample of households. (Since we are going to treat a subset of the NHANES sample as our population for this example, we ignore the complex nature of the sample design.)