A statistics professor at a large university hypothesizes that students who take statistics in the morning typically do better than those who take it in the afternoon. He takes a random sample of 36 students who took a morning class and, independently, another random sample of 36 students who took an afternoon class. He finds that the morning group scored an average of 74 with a standard deviation of 8, while the evening group scored an average of 68 with a standard deviation of 10. The population standard deviation of scores is unknown but is assumed to be equal for morning and evening classes. Let1and2represent the population mean final exam scores of statistics' courses offered in the morning and the afternoon, respectively. At the 1% significance level, does the evidence support the professor's claim?

a. No, because the test statistic is greater than the critical value

b. Yes, because the test statistic is greater than the critical value

c. No, because the test statistic is less than the critical value

d. Yes, because the test statistic is less than the critical value