A professor has two possible routes to get to work from home. The distances are not the same but for her it is all about getting to work faster. She has tried both routes, but finds it hard to tell which one on average is best, though she suspects that for route 2 there is a higher variance in the time to get to work. For a whole month, she randomly chooses one of the routes to go to work. Of 10 times that she took route 1, it took her an average of 42 minutes to get to work with a standard deviation of 5 minutes. Of 12 times that she took route 2, it took her an average of 35 minutes to get to work with a standard deviation of 9 minutes. Using statistical software, determine if there is a difference in the mean times of both routes at 5% significance. What assumptions are required to perform the test?