Question

Suppose that a the normal rate of infection for a certain disease in cattle is 25%.
To test a new serum which may prevent infection, three experiments are carried out. The
test for infection is not always valid for some particular cattle, so the experimental results are
“inconclusive” to some degree–we cannot always tell whether a cow is infected or not. The
results of the three experiments are
(a) 10 animals are injected; all 10 remain free from infection.
(b) 17 animals are injected; more than 15 remain free from infection and there are two doubtful
cases.
(c) 23 animals are infected; more than 20 remain free from infection and there are three
doubtful cases.
Which experiment provides the strongest evidence in favour of the serum? Explain your answer.

Answer 1

Here,

For the first experiments,

10 animals are injected; all 10 remain free from infection

Proportion of doutful cases = 0/10 = 0

Value of test statistics (Z) = = (0- 0.25) / Sq root of {(0.25*0.75/10)} = -1.83

For the second experiments,

17 animals are injected; more than 15 remain free from infection and there are two doubtful
cases.

Proportion of doutful cases = 2/17 = 0.1176

Value of test statistics (Z) = = (0.1176- 0.25) / Sq root of {(0.25*0.75/17)} = -1.26

For the third experiments,

23 animals are infected; more than 20 remain free from infection and there are three
doubtful cases.

Proportion of doutful cases = 3/23 = 0.13043

Value of test statistics (Z) = = (0.13043- 0.25) / Sq root of {(0.25*0.75/23)} = -1.32

Here in the above 3 experiment, the smallest test statistics is -1.83. Hence the first experiment provides the strongest evidence in favour of the serum.