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In a test given to two groups of students drawn from two normal population marks obtained were as follows,

Group A : 18, 20, 36, 50, 49, 36, 34, 49, 41.

Group B : 29, 28, 26, 35, 30, 44, 46.

Examine the equality of vacancies at 5% level of significance.

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

Marks: 8M

Year: Dec 2015

1 Answer
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Let us take the null hypothesis that the two population have the same variance i.e.

$$H_0\ :\ {\sigma }^1_i=\ {\sigma }^2_i$$ $$H_0\ :\ {\sigma }^1_i\neq \ {\sigma }^2_i$$

Alternative Hypothesis :

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$$\sum{A_i} =331$$ $$n_1=9$$

$$\sum{B_i} =236$$ $$n_2=7$$

$$\overline{A} = \sum{A_i}/n_1 = 37$$ $$\overline{B} = \sum{B_i}/n_2 = 37$$ $$S^2_1=\ \frac{\sum{{(A_i-\overline{A})}^2}}{n_1-1} = 1134/8 = 141.75$$ $$S^2_2=\ \frac{\sum{{(B_i-\overline{B})}^2}}{n_2-1} = 341.4/6 = 56.9$$ $$F = \frac{S^2_1}{S^2_2}=2.49$$

F at 5% level of significance is 3.68

F calculated is 2.49 which is less than critical value (3.68)

Hence, Null hypothesis is accepted.

$\mathrm{\therefore }$ Population have the same variance.

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