I present a sample of a diagnostic test developed for testing students who enroll into elementary statistics courses. I use the test for observational studies about correlations of students' diagnostic test scores and their subsequent performance in the observed classes. Concrete numerical statistics are given that have proved to be highly reliable and stable to a degree over different classes. The test is more precise than the common generic diagnostic/entrance tests that are administered at universities (meant to gage students' mathematical background). The test has a direct practical value since it is used in everyday teaching practice and is of wider theoretical significance since it addresses one of the components of successful education, namely influence of preparation of students on their success.