A Statistics professor has observed that for several years students score an average of 105 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, 247 students scored an average of 108 points on the final with a standard deviation of 8.8 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 a=0.05. What are the null and alternative hypotheses? Ho:| Y| V|| HA:J V] What is the test statistic? (Round to two decimal places as needed.) What is the P-value? P-value (Round to four decimal places as needed.) What is the appropriate conclusion? . Fail to reject Hy. The change is statistically significant. The software does appear to improve exam scores. . Reject Hy. The change is statistically significant. The software does appear to improve exam scores. . Fail to reject Hy. The change is not statistically significant. The software does not appear to improve exam scores. . Reject Hy. The change is not statistically significant. The software does not appear to improve exam scores. b) Does this improvement seem to be practically significant? Choose the correct answer below and fill in any answer boxes within your choice. (Round to one decimal place as needed.) A. Yes. A 95% confidence interval for the mean score using the software is ( ) ) Students' scores improved by at least 5 points on the exam. These improvements may be worth the cost of the software. ) B. No. A 95% confidence interval for the mean score using the software is ( A ) The change is not statistically significant. Students' scores may not improve at all in the long run. The software is not worth the cost. C. No. A 95% confidence interval for the mean score using the software is ( bl ) Students' scores improved by no more than 5 points on the exam. This might not be enough to justify the cost