In the academic year 2001-2002, two random samples of 25 male professors and 23 female professors from a large university produced a mean salary for male professors of $58,550 with a standard deviation of $4000; the mean for female professors was $53,700 with a standard deviation of 3200. Construct a 90% con?dence interval for the difference between the population mean salaries. Assume that the salaries of male and female professors are both normally distributed with equal standard deviations. Interpret the result.