A teacher investigates the effect of extra classes on the performance of pupils in mathematics. A group of 20 pupils receives the extra classes while a control group of 20 pupils receives singing lessons. For each of the 40 pupils the teacher calculates the increase or decrease in his or her mathematics performance by comparing the marks obtained in an examination before the extra classes to the marks obtained in an examination after the extra classes.

Which is the most appropriate

research hypothesis for the teacher to test?