Question

A 6 x 8 test of independence of susceptibility to colds and susceptibility to allergies produced a chi square of 12.51.

Write a conclusion about the two variables.

What is the critical value?

Answer 1

Given 6 x 8 test of independence of susceptibility to colds and susceptibility to allergies produced a chi square of 12.51

Question (ii)

The critical value of chi-square is calculated as follows

Number of degrees of freedom = (r-1) * (c-1)

Here r= 6, c=8

So Number of degrees of freedom = 5 * 7 = 35

Here we are not given any specific signifiacne level, so we will take the default of 0.05 significance level

The chi-square crtical value for 35 degrees of freedom and 0.05 significance level is 49.8018

Question (ii)

Null Hypothesis : There is no associaltion between susceptibility to colds and susceptibility to allergies or they both are independent

Alternate Hypothesis : There is associaltion between susceptibility to colds and susceptibility to allergies or they both are not independent

Since The chi-square crtical value of 49.8018 is greater than the chi-square test statistic of 12.51, we fail to reject the Null Hypothesis

Hence at a significance level of 0.05, we don't have sufficient evidence to reject the Null Hypothesis

Hence There is no associaltion between susceptibility to colds and susceptibility to allergies or they both are independent