Researchers conducted a study to measure the effectiveness of the drug Adderall on patients diagnosed with ADHD. A total of 112 patients with ADHD were randomly split into two groups. Group 1 included 57 patients and they were each given a dose of 15 mg of Adderall daily. Group 2 was given a daily placebo. The effectiveness of the drug was measured by testing the patients before and after and observing the mean improvement in score among the patients. Group 1 was found to have a mean improvement of 11.93 points and Group 2 had a mean improvement of 9.27 points. From past studies, the population standard deviation of both groups is known to be 6.55 points. Is there evidence to suggest that the patients taking Adderall had a higher mean improvement? Test at the 0.01 level of significance. Select the correct alternative hypothesis and state the p-value.