In a certain part of a city, the average price of homes in 2000 was $148,822, and in 2001 it was $155,908. Suppose these means were based on a random sample of 100 homes in 1997 and 150 homes in 1998 and that the sample standard deviations of sale prices were $21,000 for 2000 and $23,000 for 2001. Find a 98% confidence interval for the difference in the two population means.