An individual is considered to be overweight if his or her BMI is at least 25 (Kuczmarski et al., 1997). Consider the population of NHANES III data given in Table 15.2 (discussed in Example 15.4) and let q denote the proportion of individuals in this population who are overweight.
(a) Using the RSS sample obtained in part (a) of Problem 49, find the sample percentage, 
high, of the individuals in this RSS who are overweight. (b) Using the RSS sample obtained in part
(b) Of Problem 49, find the sample percentage, low, of the individuals in this RSS who are overweight. (c) Using the RSS sample obtained in part (c) of Problem 49, find the sample percentage, middle, of the individuals in this RSS who are overweight.
(d) Discuss the sample percentages obtained in parts (a)-(c) of this problem in conjunction with the true proportion of overweight individuals in the NHANES III population.
(e) Compare the results obtained in this problem with those obtained in Problem 49. (See Chen, Stasny, and Wolfe (2006b) for more discussion about the use of unbalanced RSSs in estimation of population proportions.)
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.)