It’s that time of the year again – final exams have rolled around and, as a tutor, I’m sitting around marking them. Exam marking can be an extremely depressing or entertaining process, depending on the state of mind and quality of the exams being marked.

I thought it would be interesting to document here my thoughts on the general things that people get wrong, and this can be instructive for students and teachers alike.

1.The Central Limit Theorem means that all samples are Normally distributed.

I had to start with the Central Limit Theorem, I’m not sure that there is anything less well understood as the CLT in undergraduate statistics. Let’s be clear, the Central Limit Theorem says that if our sample size is large, then the sample mean has a Normal distribution. The sample itself does not.

2.Using sample parameters in hypotheses

I see a lot students including things like

$latex H_{0}:\bar{X}=50$

and students do not seem to understand the significance of the hypothesis test. Doing this implies we’re checking to see if our sample mean is 50, this is easily checked by inspection, and not very interesting. Students who do this are failing to see the bigger picture, which is we’re using our sample to check if the unknown population mean is equal to 50, this is much cooler!

3.Not checking their understanding

Statistics is a branch of mathematics, which at its base is logic. If it seems like magic, or if it doesn’t make sense to you, I’d check your understanding. Ask questions and be curious, use your teacher’s office hours. I promise it will make sense eventually.