Question

A sample of 300 students of undergraduate and 300 students of postgraduate classes of a university were asked to give their opinion towards autonomous colleges. 190 of the undergraduate and 210 of the postgraduate students favoured the autonomous status.

i) At 5% significance level, would it be said that the opinions of the undergraduate and postgraduate students on autonomous colleges are independent? {The critical value of the requisite test statistic is 3.84} (

ii) What is the implication / interpretation of your results in 3) i) above?

Answer 1

Solution:

We can put the given information in below tabular form:

	Undergraduate	Postgraduate	Total
Favour	190	210	400
Not Favour	110	90	200
Total	300	300	600

The null and alternative hypotheses are:

The opinions of the undergraduate and postgraduate students on autonomous colleges are independent.

The opinions of the undergraduate and postgraduate students on autonomous colleges are not independent.

Under the null hypothesis, the test statistic is:

Where:

O is the observed frequencies

E is the expected frequencies

The expected frequencies are counted as:

ii) Since we fail to reject the null hypothesis at the 0.05 significance level, we, therefore, conclude that the opinions of the undergraduate and postgraduate students on autonomous colleges are independent