Patients with pleural infection were randomly assigned to be given either an active medical treatment (n = 52) or a placebo (n = 55). One outcome that was measured on each patient was duration of hospital stay. Consider conducting a t test of the null hypothesis that average hospital stay is the same for treatment and for control. Assuming that there are 57 degrees of freedom for the test, what is the distribution of the test statistic if the null hypothesis is true?