On the Hypothesis Testing Procedure for Both Parameters of the Binomial Distribution

Kaur, Jasmine
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Faculty of Graduate Studies and Research, University of Regina

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.

A Thesis Submitted to the Faculty of Graduate Studies and Research In Partial Fulfillment of the Requirements for the Degree of Master of Science in Statistics, University of Regina. vii, 51 p.