Hypothesis testing for arbitrary bounds

I derive a rigorous method to help determine whether a true parameter takes a value between two arbitrarily chosen points for a given level of confidence via a multiple testing procedure which strongly controls the familywise error rate. For any test size, the distance between the upper and lower bounds can be made smaller than that created by a confidence interval. The procedure is more powerful than other multiple testing methods that test the same hypothesis. This test can be used to provide an affirmative answer about the existence of a negligible effect.