Our aim in this short paper is therefore to derive the coverage probability and its
expected length of the new confidence interval compared to the well known WS
confidence interval. Typically, a confidence interval with a minimum coverage probability
1-α, when α is a level of significance, and a shorter expected length is preferable.
The paper is organized as follows. Section 2 presents confidence intervals for
the difference of two normal population means with one variance unknown. Coverage
probabilities and expected lengths of confidence intervals in Section 2 are derived in
Section 3. Section 4 gives simulation results of coverage probabilities and the ratio of
expected lengths of confidence intervals for the difference between two normal
population means with one variance unknown for selected samples sizes with a range of
values of known ratio of variances. Section 5 contains a discussion of the results and
conclusions.