STATISTICS 2MA3
(b) What pivotal quantity is used
to compare two variances? Under what assumptions is it valid?
Write out the confidence interval formula derived from it, using
Rosner's notation for the quantiles of the F distribution.
[7 marks]
(c) Give 5 interesting
facts about William Sealy Gosset. [3 marks]
(a) Students randomly assigned 22 giant freshwater prawns to two different aquaria and recorded their weight in grams after 25 days.
Tank A: 0.85 0.94 0.82 1.19 0.52 1.14 0.76 1.59 1.11 0.66 0.76 Tank B: 1.47 0.64 0.79 1.95 0.82 0.94 0.71 0.94 0.70 0.70 0.84
(b) A random sample of 10 patients was treated with an anti-inflammatory cream on one arm (the left or right arm was chosen at random) and a placebo cream on the other arm. After 4 days a measure of muscle soreness was taken for each patient on each arm.
Patient: 1 2 3 4 5 6 7 8 9 10 Placebo: 46 22 10 14 26 29 29 47 20 13 Treated: 2 32 30 3 14 32 2 39 18 2