A survey study is a research method commonly used to quantify population characteristics in biostatistics and public health research, two fields that often involve sensitive questions. However, if answering sensitive questions could cause social undesirability, respondents may not provide honest responses to questions that are asked directly. To mitigate the response distortion arising from dishonest answers to sensitive questions, the randomized response technique (RRT) is a useful and effective statistical method. However, research has seldom addressed how to apply the RRT in public health research using an online survey with multiple sensitive questions. Thus, we help fill this research gap by employing an innovative unrelated question design method. To illustrate how the RRT can be implemented in a multivariate analysis setting, we conducted a survey study to examine the factors affecting the intention of illegal waste disposal. This study demonstrates an application of the RRT to investigate the factors affecting people's intention of illegal waste disposal. The potential factors of the intention were adopted from the theory of planned behavior and the general deterrence theory, and a self-administered online questionnaire was employed to collect data. Using the RRT, a covariance matrix was extracted for examining the hypothesized model via structural equation modeling. The survey results show that people's attitude toward the behavior and their perceived behavioral control significantly positively affect their intention. This paper is useful for showing researchers and policymakers how to conduct surveys in environmental or public health related research that involves multiple sensitive questions.