Mumbai University > Mechanical Engineering > Sem 4 > Applied Mathematics IV

Marks: 8M

Year: May 2014

Observed frequency:

Expected frequency:

Step 1:

Null Hypothesis $$(H_0)\ The\ performance\ in\ Mathematics\ is\ independent\ of\ performance\ in\ Physics.$$

Alternative Hypothesis : The performance in Mathematics is not independent of performance in Physics.

Step 2 :

L.O.S : 5%

Degree of freedom = (r-1)(c-1) = (3-1)*(3-1) = 4

Hence, Critical value ($X^2_{\propto }$) = 9.4877

Step 3 :

$$X^2_{cal}=\ \sum{\frac{{(O-E)}^2}{E}} = 140.3943$$

Step 4: Decision :

Since $X^2_{cal}\gt\ X^2_{\propto }$ , $H_0\ $is rejected.

Hence , the performance in Mathematics is not independent of the performance in Physics.