A school district wants to determine whether a new math curriculum improves student test scores. They randomly assign 30 of 60 volunteer classrooms to the new curriculum and the remaining 30 continue with the traditional curriculum. After one semester, the mean score for the new curriculum group is 78.4 with standard deviation 8.2, and the mean for the traditional group is 74.1 with standard deviation 9.0 (both n = 30). (a) State the null and alternative hypotheses for a two-sample t-test. (b) Calculate the test statistic and approximate p-value. Show all work. (c) At α = 0.05, state your conclusion in context.