Let \(Q_ N\) be a population of \(N\) balls bearing real numbers \(a_{N1},\dots, a_{NN}\). Draw \(n=n_ N\) balls from \(Q_ N\) randomly without replacement, and denote the numbers appearing on these \(n\) balls by \(X_ 1,\dots, X_ n\). Write \(p= n/N\), \(q=1-p\), \[ \begin{alignedat}{2} \mu_ N &= EX_ 1= N^{-1} \sum^ N_{j=1} a_{Nj}, \qquad &\sigma^ 2_ N &= N^{-1} \sum^ N_{j=1} (a_{Nj}- \mu_ N)^ 2,\\ \overline{X}_ N &= n^{-1} \sum^ N_{j=1} X_ j, &\widehat{\sigma}^ 2_ n &= (n-1)^{-1} \sum^ N_{j=1} (X_ j- \overline{X}_ n)^ 2. \end{alignedat} \] Throughout this paper we assume that \(\sigma_ N>0\) and \(0<p<1\). For simplicity, we write \(a_ j\), \(\mu\), \(\sigma\), \(\overline{X}\), \(\widehat{\sigma}\) for \(a_{Nj}\), \(\mu_ n\), \(\sigma_ N\), \(\overline{X}_ n\), \(\widehat{\sigma}_ n\) and so on. Let \(\Phi(\cdot)\) be the distribution function of the standard normal \(N(0,1)\). It is proved by Th. Höglund [Scand. J. Statistics, Theory Appl. 5, 69-71 (1978; Zbl 0382.60028)] that \[ \sup_ x | P(\sqrt{n} (\overline{X}- \mu)/ (\sigma \sqrt{q})\leq x)- \Phi(x)|\leq C(Npq)^{-1/2} E| X_ 1|^ 3/ \sigma^ 3. \] We denote by \(C\) a constant which may take different values in different places. We establish a similar bound for the finite-population \(t\)- statistic \(t_ n= \sqrt{n} (\overline{X}- \mu)/ \widehat{\sigma} \sqrt{q}\).