Examples Sheet 2
Here is more feedback from my bunch of 21 students.
Sheet 2.
1. Everyone was OK
2. Mostly fine; a few didn't know how to size the test
3. 1/3 couldn't size the test
4. 1/2 couldn't construct the test at all; most of the rest just
assumed that the optimal test was a LRT. Only two got the point about
UMP: most of them didn't understand what it meant.
5. Most got the test right, but couldn't find the distribution of T
(even though it was in the notes). Four had pretty much totally
misunderstood what a likelihood ratio was (ie they only optimized over
the parameters for the null hypothesis).
6. Most managed to construct the test. They were able to quote "2 log
LR is distributed like chi-squared", but didn't seem to realise that
this held only under H0 and that under H1 it tended to be larger.
7-12. About three quarters had trouble working out degrees of freedom.
About one quarter had trouble working out expected values. They were
all able to plug numbers into formulae from the notes, which made them
come unstuck in Question 9 when they only counted 6 categories. I was
disappointed not to get any long answers on why Statistics is an
absurd subject... and there were very few careful answers to the
descriptive parts of Questions 10 and 11.
13. The few who attempted it had no trouble.