Question

My fourth question

A social worker wished to determine if the race of loan applicants was independent of the approval of loans. The following table presents the results of her survey:

Applicants for Loans

Ethnicity	Approved	Rejected
Caucasian	213	189
Black	374	231
Asian	358	252

Conduct the appropriate hypothesis test that will provide an answer to the social worker. Use a significance level of 0.01.

Answer 1

As we are testing here whether the race of loan applicants was independent of the approval of loans, therefore this is a chi square test of independence. The expected values for each of the 6 cells here is computed as:

E_i = (Sum of row i)*(Sum of column i) / Grand Total

The chi square test statistic contritbuion for each of the 6 cells here is computed as:

The computations here are made as:

The circular bracket here contains the expected value while the square bracket contains the chi square test statistic contribution here.

The chi square test statistic for the test here is computed as:

the degrees of freedom is computed here as:
Df = (num of columns - 1)*(num of rows - 1) = 2

Therefore the p-value for the test here is computed as:

As the p-value here is 0.02041 > 0.01 which is the level of significance, therefore the test is not significant here and we cannot reject the null hypothesis here. Therefore we have insufficient evidence here that the two variables are associated here.