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 colleges are independent of the level of classes of students.

Answer 1

Answer on Question #39546, Math, Other

Let $n_1 = n_2 = 400$ be the number of students in each group, $x_1 = 290$ and $x_2 = 310$ – the number of students that favoured the autonomous status. We will use proportion z test to find out whether the opinion is independent of the level of classes of students.

$$H_0: p_1 = p_2$$ $$H_1: p_1 \neq p_2$$

where $p_1 = \frac{x_1}{n_1} = 0.725$ and $p_2 = \frac{x_2}{n_2} = 0.775$.

Pooled proportion:

$$p = \frac{x_1 + x_2}{n_1 + n_2} = 0.75$$

Test statistic:

$$z = \frac{p_1 - p_2}{\sqrt{p(1 - p)\left(\frac{1}{n_1} + \frac{1}{n_2}\right)}} = -1.633$$

Critical values:

$$z_{1,2} = \pm 1.96$$

Since z is not in the rejection region, we don't reject null hypothesis.

ANSWER: There is not enough evidence to conclude that the opinion regarding autonomous status of colleges are dependent of the level of classes of students.