Business Context

LendWise is building a loan-loss forecasting model. Before using a portfolio default-rate assumption of 2.0% in the model, the risk team wants to test whether recent observed performance is consistent with that assumption.

Problem Statement

You are given a random sample of recently issued loans and whether each loan defaulted within 12 months. Determine whether the historical assumption that the true default rate is 2.0% is still reasonable.

Given Data

Assume the sample is representative and large enough for a normal approximation to the binomial.

Requirements

1. State the null and alternative hypotheses for testing the model assumption.
2. Compute the sample default rate.
3. Calculate the standard error under the null hypothesis.
4. Compute the z-statistic and two-sided p-value.
5. Build a 95% confidence interval for the true default rate.
6. Conclude whether the 2.0% assumption is reasonable to use in the model.

Assumptions

• Each loan outcome is independent.
• The 2,500 loans are a random sample from the population relevant to the model.
• Default is a binary outcome, so a binomial model applies.
• Use a two-sided test because the assumption could be too low or too high.