Rosner, Willett, and Spiegelman, in "Correction of Logistic Regression Relative Risk Estimates and Confidence Intervals for Systematic Within-Person Measurement Error" [Statistics in Medicine (1989) 8:1051-1070], describe a nurses' health study in which the diet of a large sample of women was examined. One of the objectives of the study was to determine the percentage of calories from fat (PCF) in the diet of a population of nurses and compare this value with the recommended value of 30%. The most commonly used method in large nutritional epidemiology studies is the food frequency questionnaire (FFQ). This questionnaire uses a carefully designed series of questions to determine the dietary intake of participants in the study. In the nurses' health study, a sample of nurses completed a single FFQ. These women represented a random sample from a population of nurses. From the information gathered from the questionnaire, the PCF was then computed. The researchers decided that the main variable of interest was the percentage of calories from fat in the diet of nurses. The parameters of interest were the PCF mean μ for the population of nurses, and the PCF for the population of nurses. They wanted to determine if the average PCF for the population of nurses exceeded the recommended value of 30%.
1. (1.5 points) Defining the problem.
a. (0.5 points) What is the population of interest?
b. (0.5 points) What dietary variables may have an effect on a person's health?
c. (0.5 points) What hypotheses are of interest to the researchers?
2. (1 point) Determine the sample size required to meet certain specifications imposed by the researcher.
In order to estimate these parameters and test hypotheses about the parameters, it was first necessary to determine the sample size required to meet certain specifications imposed by the researchers. The researchers wanted to estimate the mean PCF with a 95% confidence interval having a tolerable error of From previous studies, the PCF values ranged from 10% to 50%. Because we want a 95% confidence interval with a width of 3.