Two types of chemical solutions, X and Y, were tested for their pH (degree of acidity of the solution). Analysis of 6 samples of X showed a mean pH of 6.72 with a standard deviation of 0.024. Analysis of 5 samples of Y showed a mean pH of 6.49 with a standard deviation of 0.032. Using a 0.05 significance level, determine whether the two types of solutions have different pH values.

On an examination in psychology 12 students in one class had a mean grade of 78 with a standard deviation of 6, while 15 students in another class had a mean grade of 74 with a standard deviation of 8. Using a significance level of 0.05, determine whether the first group is superior to the second group.