Question

calculate the X2 and test whether the two attributes are independent at 5% level of significance

Answer 1

A chi-squared test, also written as $\chi^2$ test,is a statistical hypothesis test that is valid to perform when the test statistic is chi-squared distributed under the null hypothesis, specifically Pearson's chi-squared test and variants thereof. Pearson's chi-squared test is used to determine

 whether there is a statistically significant difference between the expected frequencies 

and the observed frequencies in one or more categories of a contingency table.

The formula for $\chi^2$ is given by-

$\chi^2=\sum\dfrac{(O_f-E_f)^2}{E_f}$

Where $O_f=$ Observed frequency of samples

$E_f=$ Expected frequency of samples

At 5% level of significance, The value of $\chi^2$ test is generally lies between $0.1232 \text{to} 0.6754$

It also depends upon the degree of freedom.