Historically, 10% of all loans approved by a large bank have gone into default. Stockholders respond to this by choosing a new bank president with new ideas on how loans should be dispersed. Over a five-year period in which the new president has been in charge, the bank issues 11,000 loans. A random sample of 400 loans during this period is chosen, of which 29 were found to be in default. Perform a hypothesis test to see whether the new president has caused the proportion of loans in default to decline.
1) State the null and alternative hypothesis.
2) Compute the sample proportion, Test Statistic, and p-value.
3) At a 0.05 significance level perform a hypothesis test to see whether the new president has caused the proportion of loans in default to decline. State your conclusion in terms of this problem and report the p-value for this hypothesis test.