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In an experiment on immunization of cattle from Tuberculosis the following results were obtained

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Use $x_2$ Test to determine the efficiency of vaccine in preventing tuberculosis.

Mumbai University > COMPS > Sem 4 > Applied Mathematics 4

Marks : 06

Year : MAY 2015

1 Answer
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1) Calculation of test statistic on the basis of this hypothesis the number in the first cell $=\dfrac {A\times B}N$

A = Total in first column

B = Total in first row

N = Total no. of observation

Number in the first cell = $\dfrac {1024\times 294}{1206}\\ = 249.63 \\ = 250$

2) Level of significance a $= 0.05$

3) Degree of freedom $= (x - 1)(x - 1) = (2 - 1)(2 -1)\\ = 1$

Having obtained the expected frequency in the first cell since the total remains the same the figure in other cell can be easily obtained.

$294 – 250 =44\\ \space \&\space 1024 – 250 = 774 \space \&\space 182 – 44$

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4) Critical value: For 1 degree of freedom of 5% level of significance the table value of $x^2 = 3.84$

Calculation of $(O - E)^2/ E \space i.e\space x^2.$

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5) Decision:- Since the calculated value of $x^2 = 10.186$ is greater than the table value $x^2 = 3.84.$

The hypothesis is rejected.

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