17 students in a class are assigned to a new method of teaching science. After 6 weeks in the classroom, they are given a test accessing their knowledge of basic science concepts to see if the teaching has been effective. The result is: =84, SD=16, N=17. Previously the students in that class had a mean of 78 on this exam (N=78). Is the difference after 6 weeks of instruction consistent with what is likely under conditions of chance above or does it likely reflect a difference?
The new instructional method does reflect a difference since the students have recorded an improvement in the subject, from a mean of 78 to 84.