Neatly hand write your solutions - marks will be assigned for presentation
1. In an experiment on human behaviour, a sociologist asks four men and four women to enter a room and sit wherever they wish at a rectangular table. There are three chairs at each side of the table and one at each end. The two end seats are considered to be special in that people sitting there have more dominant positions at the table.
The seating experiment is repeated 28 times using new subjects each time. The following table shows the numbers of times that the two end seats were occupied by two men, by two women and by a man and a woman.
Using a Likelihood ratio test, test the hypothesis that the probabilities for the three classes are:
3/14, 3/14 and 8/14.
Occupants of end seats
MM
FF
MF or FM
Total
Observed frequency
9
4
15
28
2. A seed dealer claims that his sweet pea seeds have a germination rate of 80%. A customer purchased 4 packages of sweet pea seeds, one package of each of four colours. He planted 100 seeds from each package. The number of seeds germinating within one month were as follows:
Red
White
Blue
Yellow
Germination
76
66
81
74
No germination
24
34
19
26
(a) Using a Likelihood Ratio Test, test the hypothesis that the germination rate is 80% for all four of the colours.
(b) Using a Likelihood Ratio Test, test the hypothesis that the germination rate is the same for all four colours, but not necessarily 80%.
3. Six hundred and four adult patients in a large hospital were classified according to whether or not they had cancer, and according to whether or not they were smokers. The results were are given below.
Using a Likelihood Ratio Test, test the hypothesis that the disease classification is independent of the smoking classification.
Cancer patient
Other
Smoker
72
397
Non-smoker
10
125
1
