SummaryUsing asymptotic expansions of the Kummer hypergeometric function, the sequential. F‐test criterion is evaluated asymptotically in terms of the sample size. The continuation region inequalities for the test are inverted and expressed in terms of known test criteria. A rapidly converging algorithm for carrying out the sequential procedure is provided. This makes theF‐test easier for the practitioner to use. Almost sure finite termination of the sequential. F‐test is asserted by appealing to the continuation inequalities and a heuristic asymptotic expansion of the test criterion. Average stopping times of the sequential procedure for a variety of population means and population number configurations are tabulated. The computer symbolic manipulation program MAPLE was used to derive some for