||Error in measuring exposure variable is a common concern in all etiologic research. There has been increasing acknowledgment of the importance of measurement error in epidemiology. In addition, binary response arising in many fields of study is common in both biological and social sciences. Much of the recent biostatistical and epidemiological literature has concerned the association between a binary response and exposure. In the epidemiologic studies, calculation of sample size and statistical power are essential ingredients. This Thesis, therefore, adopts a hypothesis testing based on the method of maximum likelihood approach to approximate sample sizes which are needed to test hypothesis on association between a continuous exposure and a categorical variable on a binary outcome variable at a specified significance level and power against given alternatives for a logistic regression model when the explanatory variables are measured with errors.