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. Please be sure to clearly state the null and alternative hypotheses, critical value, test statistic, and conclusion.

Answer 1

Answer to the question)

Given the numbers:

.

Let us calculate the expected values for it

E = row total * column total / grand total

For example for first cell

row total = 402 , column total = 945 and grand total = 1617

Expected value for cell 1 = 402*945 /1617 = 234.94

Likewise all the expected values are shown as below:

.

Now we use the chi square test , and find chi square statistic

Chi square statistic = sum of [(O - E)^2/ E ]

The calculations are as shown below:

.

Inference: Since P value 0.0407 > alpha 0.01 , we fail to reject the null hypothesis

Conclusion: thus there is no significant evidence to conclude that ethnicity and the approval of loans are dependent on each other. Hence we conclude that the two variables are independent of each other.