Term of Award

Summer 2014

Degree Name

Master of Science in Mathematics (M.S.)

Document Type and Release Option

Thesis (restricted to Georgia Southern)

Department

Department of Mathematical Sciences

Committee Chair

Charles W. Champ

Committee Member 1

Andrew V. Sills

Committee Member 2

Broderick O. Oluyede

Abstract

A new method is given for testing if there is a difference between two population proportions. The size of the test is exact in the sense that it is the maximum probability of rejecting a true null hypothesis. A method is given for determining a greatest lower bound on the power of the test over a region in which the difference in the two population proportions is at least a given value between zero and one. A specified greatest lower bound for the power by the researcher is used to determine the minimum total sample size needed. A comparison is made with a commonly used approximation method. We demonstrate that the actual size of the test for the approximation method is greater than the specified size while our new method has a size of no more the specified size. Further, the recommended method for determining the minimum total sample size for the approximation method is, in general, greater than what is needed by our new test. Some examples are given.

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