The concept of differential privacy as a rigorous definition of privacy has emerged from the cryptographic community. However, further careful evaluation is needed before we can apply these theoretical results to privacy preservation in everyday data mining and statistical analysis. In this paper we demonstrate how to integrate a differential privacy framework with the classical statistical hypothesis testing in the domain of clinical trials where personal information is sensitive. We develop concrete methodology that researchers can use. We derive rules for the sample size adjustment whereby both statistical efficiency and differential privacy can be achieved for the specific tests for binomial random variables and in contingency tables.