Do private school students obtain higher marks than public school students? To evaluate this question we collected a sample of Australian Tertiary Admission Rank (ATAR) data from 2014. We obtained a mean ATAR of 76.5 with a standard deviation of 12 from a sample of 54 private school students. A sample of 32 public school students had an average ATAR of 74.7 and standard deviation of 10.

Using the 0.01 level of significance, is there sufficient evidence that private school students obtain a higher ATAR than public school students?