Previous results on the sampling properties of test reliability coefficients are rather scarce. Most existing methods for reliability estimation are derived from parametric relationships by substitution of sample statistics for parameters. The statistical properties of estimators so obtained remain largely unknown. The present study is intended as a contribution to the sampling theory of reliability estimation under normality assumptions when a total test has been split into two, not necessarily parallel, parts. A maximum-likelihood ratio test of a point hypothesis concerning the parameter value of coefficient alpha is derived. This method is then converted to yield confidence limits for the parameter at any chosen level of confidence. Worked examples are appended by way of illustration.