EXAMPLE 9.12 Sampling in the Adequate Calcium Today (ACT) Study

The ACT study was designed to examine relationships among bone growth patterns, bone development, and calcium intake. There were more than 15,000 adolescent participants from six states: Arizona (AZ), California (CA), Hawaii (HI), Indiana (IN), Nevada (NV), and Ohio (OH). After the major goals of the study were completed, the investigators decided to do an additional analysis of the written comments made by the participants during the study. Because the number of participants was so large, a sampling plan was devised to select sheets containing the written comments of approximately 10% of the participants. A systematic sample (see page 141) of every 10th comment sheet was retrieved from each storage container for analysis.⁵ Here are the counts for each of the six states:

471

There were 1567 study participants in the sample. We use the proportions of students from each of the states in the original sample of more than 15,000 participants as the population values.⁶ Here are the proportions:

Let's see how well our sample reflects the state population proportions. We start by computing expected counts. Because 10.5% of the population is from Arizona, we expect the sample to have about 10.5% from Arizona. Therefore, because the sample has 1567 subjects, our expected count for Arizona is

Here are the expected counts for all six states: