The mortgage department of a large bank is interested in nature of loans of first time borrowers. This information will be used to tailor their marketing strategy. They believe that 50% of first-time borrowers take out smaller loans than other borrowers. Test to determine if the percentage is the same. They sample 100 first time borrowers and find that 61 of these loans are smaller that the other borrowers. Use a 5% level of significance. a. Test the claim
b. Construct a 95% confidence level for the proportion of first time smaller borrowers than other borrowers.