written 7.7 years ago by | • modified 7.7 years ago |
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
written 7.7 years ago by | • modified 7.7 years ago |
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
written 7.7 years ago by |
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.
$294 – 250 =44\\ \space \&\space 1024 – 250 = 774 \space \&\space 182 – 44$
4) Critical value: For 1 degree of freedom of 5% level of significance the table value of $x^2 = 3.84$
Calculation of $(O - E)^2/ E \space i.e\space x^2.$
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.