6. The nation’s 40,000 mortgage brokerages are some of the most profitable small businesses in the United States. These low-profile companies find loans for customers in exchange for commissions. Mortgage Bankers Association of America provides data on the average size of loans handled by mortgage brokerages (The Wall Street Journal, February 24, 2003).

The CD file named Mortgage contains data from a sample of 250 loans made in 2001 and a sample of 270 loans made in 2002 that are consistent with these data. Based on historical loan data, the population standard deviations for the loan amounts can be assumed known at $55,000 in 2002 and $50,000 in 2001. Do the sample data indicate an increase in the mean loan amount between 2001 and 2002? Use α  .05.