Abstract
The main purpose of this paper is to perform the hypothesis tests of parameters \(p\) and \(m\) (both are unknown) of the binomial distribution. Delta method and the moment generating function are used to derive the important statistic \(X^{2}_{2}(p,m)\) for the hypothesis testing based on its asymptotical distribution. The probability of type I error and the power of the test are calculated, which are the main parts of this research. For the hypothesis testing, we consider the null hypothesis \(H_{0}\) : \(p=p_{0}\) , \(m=m_{0}\) with a significant level \(\alpha=0.05\) . The 3-D figures of the type I error and the power of the test are used to test of the null hypothesis \(H_{0}\) .
