In the academic year 1997-1998, 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 and an average for female professors of $53,700 with a standard deviation of $3200. At the 5% significance level, can you conclude that the mean salary of all male professors for 1997-1998 was higher than that of all female professors? Assume that the salaries of male and female professors are both normally distributed with equal standard deviations.