About 74% of Freddie Mac–owned loans were refinanced in the second quarter of 2005 (USA Today, Lifeline, August 3, 2005), resulting in new mortgages carrying loan amounts at least 5% above the original mortgage balance. The median loan refinanced in the second quarter was 2.6 years old. If a sample size of 2,500 was used to obtain this information,

a. Determine if the sample size for the test is large enough to warrant approximating the sample proportion’s distribution with a normal distribution.

b. Use this information to determine if less than 75%

of new mortgages had a loan amount at least 5%

above the original mortgage balance. Use a test statistic approach with a  0.025.