Consider a sample from a normal population with mean, μ, and variance unknown. Suppose it is desired to test H0:μ ≤ μ0 versus H1:μ ≥ μ1, with the region HI1:μ0 < μ < μ1 being a (nonempty) indifference zone. It is shown that the usual Student's t-test is inadmissible for this problem. An alternative test is proposed. The two sided problem with indifference region is also discussed. By contrast with the above result, the usual Student's t-test is admissible here. However the two sided version of the alternative test mentioned above does offer some practical advantages relative to the two sided t-test. A 3-decision version of the two sided problem is also discussed. Here the t-test is inadmissible, and is dominated by the appropriate version of the alternative test. The results concerning tests are also reformulated as results about confidence procedures.