On the Hypothesis Testing Procedure for Both Parameters of the Binomial Distribution
The main purpose of this thesis 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 α=0.05. The rejection region was considered to be: X_2^2 (p_0,m_0 )>χ^2 (α), where χ^2 (α) is the quantile of the chi-square distribution with 2 degrees of freedom. 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.