Hollander, Park and Proschan (1986) proposed a test of new is better than used of a specified age. It is based on large sample normality of the test statistic. There is, however, no study in the literature on its actual size for small and moderate sample sizes. To shed some lights on this, the results of a Monte Carlo simulation study as well as two real data examples are reported and these indicate that the test can have a quite liberal size, especially for small to moderate sample sizes. In order to improve on this weakness, a modified test is proposed and studied. It is noticed that this modified test seems to over-correct the original test to an extent that it becomes unduly conservative sometimes. Hence we propose another modification that combines the original test and the modified test turns out to have its size quite close to the nominal level and is therefore preferable to both the original and modified tests.