Suppose a statistics professor believes that there is a significant difference between the mean class scores of statistics students in section 1 vs. students in section 2. The professor thinks that the scores of section 2 are larger than those of section 1 by 5 points. He takes random samples from each of the populations. The mean and sample standard deviation for 12 statistics students from section 1 were 75.86 and 6.91. The mean and sample standard deviation for 5 statistics students from section 2 were 83.41 and 9.73.

Based on these data, should the professor conclude that the student's scores in section 2 are larger than those in section 1 by 5 points? Use your knowledge of statistics to conclude.