One of the criteria statistics professors use to select a textbook is the number of exercises provided. One particular topic in statistics is selected: the t-test of the mean. A random sample of 15 professors is asked how many exercises students should do in order to master the topic. The sample average was 19.2, with a standard deviation of 5.2. A random sample of 20 students who demonstrated that they had mastered the topic by successfully completing some related questions was selected from these professors' classes. The students were asked how many exercises they actually completed for this topic. The sample average was 12.3, with a standard deviation of 3.6.Is there evidence, at the 1% level of significance, that the professors overestimate the number of exercises that students need to do to master this topic? You may assume the sample data for both professors and students appear normally distributed.