l. The mortgage departlnent of a large bank is interested in the nature of loans of rst-time borrowers. This information will be used to tailor their marketing snamgy. They believe that 511% of rst-time borrowers take out smaller loans than other borrowers. They perform a hypothesis ten to determine if the percentage is the same or differcnt from 50%. They sample 11)!) rst-time borrowers and find 53 of these loans are smaller than the other borrowers. For the hypothesis test they choose a 5% level of signicance. 2. A manufacturer of running shoes knows that the average lifetime for a particular model of shoes is 15 months. Someone in the reaearch and development division of the shoe company claims to have developed a longer lasting product. This new pmduct was worn by 3!} individuals and lasted on average for 1? months. The variability of the original shoe is estimated based on the standard deviation of the new group which is 5.5 months. Is the designer's claim of a better shoe supported by the trial results? Please base your decision on a using a level of signicance of 5%