Question

a sample of 400 students of undergraduate and 400 students of post graduate classes were taken to know their opinion about autonomous college. 290 of the undergraduate and 310 of the post graduate students favoured the autonomous status. Present these fact in the form of a table and test at 5% level, that the opinion regarding autonomous status of college are independent of the level of classes of students.

Answer 1

Answer on Question #42914 – Math - Statistics and Probability

A sample of 400 students of undergraduate and 400 students of post graduate classes were taken to know their opinion about autonomous college. 290 of the undergraduate and 310 of the post graduate students favoured the autonomous status. Present these fact in the form of a table and test at 5% level, that the opinion regarding autonomous status of college are independent of the level of classes of students.

Solution

$H_0$: The opinion regarding autonomous status of college is independent of the level of classes of students.

$H_1$: The opinion regarding autonomous status of college is dependent of the level of classes of students.

L. O. S. = 5%.

Test statistic (see http://math.hws.edu/javamath/ryan/ChiSquare.html)

$$\chi^2 = \frac{N(ad - bc)^2}{(a + b)(c + d)(a + c)(b + d)} = \frac{800(290 \cdot 90 - 110 \cdot 310)^2}{(290 + 110)(310 + 90)(290 + 310)(110 + 90)} = 2.67.$$

Table value:

$$\chi_{(2-1)(2-1)df}^2 = \chi_{(1)df}^2 = 3.84 \text{ at } 5\% \text{ L. O. S.}$$

Inference

$$\chi_{calc}^2 < \chi_{tab}^2$$

We accept the null hypothesis. The opinion regarding autonomous status of college is independent of the level of classes of students.

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