Question

Assume that a Chi-square test was conducted to test the goodness of fit to a 3:1 ratio and that a Chi-square value of 2.62 was obtained (Table value is equal to 3.84). Should the null hypothesis be accepted? How many degrees of freedom would be associated with this test of significance?

Answer 1

Chi square test was conducted to test goodness of fit of a 3: 1 ratio

Since, chi square value is calculated by (O-E)2 /E ( where O is observed value and E is expected value

We accept the null hypothesis if chi square value is less than the critical value given in the table at a particular degree of freedom- then we accept the null hypothesis

If chi square value is greater than ( which means deviation in observed value is quite high) then we reject our null hypothesis.

Here, the chi square value is 2.68 which is less than the critical value given in the table which is 3.84.

2.68<3.84 (critical value)

Therefore,the null hypothesis should be accepted and the given data fits the model.

Since, the ratio is 3:1 it means there are only two variables here ( like as a random example if the ratio would have been 3:1:1 then there would have been three variables).

Degree of freedom is calculated by the formula= n-1 ( where n is number of variables)

So, degree of freedom = 2-1

= 1

So, in the above case degree of freedom is only 1.