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Stat261 Assignment #4

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Stat261
Assignment #4
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
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