A random sample of 8 students was selected from the senior class at each of four large high schools, and the score of each of these 32 students on a certain mathematics exam was observed. Suppose that for the 8 students from each school, the sample mean and sample variance of the scores were as shown in the Table below. Test the hypothesis that the senior classes at all four high schools would perform equally well on this exam. Carefully discuss the assumptions that you are making in carrying out the test.

School Sample Sample Mean Variance 1 105.7 30.3 2 102.0 54.4 3 93.5 25.0 110.8 36.4