A Statistics professor has observed that for several years students score an average of 114 points out of 150 on the semester exam. A salesman suggests that he try a statistics software package that gets students more involved with computers, predicting that it will increase students' scores. The software is expensive, and the salesman offers to let the professor use it for a semester to see if the scores on the final exam increase significantly. The professor will have to pay for the software only if he chooses to continue using it. In the trial course that used this software, 206 students scored an average of 117 points on the final with a standard deviation of 8.6 points. Complete parts a) and b) below. a) Should the professor spend the money for this software? Support this recommendation with an appropriate test. Use alphaequals0.05.