Question

1. A bank has recently acquired a new branch and thus has customers in this new territory. They are interested in the default rate in their new territory. They wish to test the hypothesis that the default rate is different from their current customer base. They sample 200 files in area A, their current customers, and find that 20 have defaulted. In area B, the new customers, another sample of 200 files shows 12 have defaulted on their loans. At a 10 % level of significance, can we say that the default rates are the same or different?

Answer 1

Here we're testing:

The pooled sample proportion is given by:

, where n_A and n_B is the sample size of area A and B respectively and p_A and p_B is the sample default rates of area A and B.

The standard error is given by:

, and the test statistic is given by:

. Now using the values i.e. n_A = n_B = 200 and p_A = 0.1 and p_B = 0.06 we get p = 0.08 SE = 0.027 and Z = 1.4744. At a level 10% the critical value is Z_0.95 = 1.645. Now as the test statistic is less than the critical value we fail to reject the null hypothesis, i.e. there is not enough evidence to support the claim that two default rates are different.