An educational researcher is interested in determining whether calculus students who study with music playing perform differently from those who study with no music playing.
a. She asks for volunteers to participate in the study and finds a large number of students who study with music playing and a large number who study with no music playing. She then compares the mean scores on the next calculus exam, using a t-test. Is this an appropriate design and analysis for the problem at hand? Explain your reasoning.
b. Realizing that the abilities and backgrounds of the students might be important in this study, the researcher pairs students (one student to each treatment group) from the volunteer groups on the basis of their current grade in the class. She then compares the mean scores on the next calculus exam, using a t-test. Is this an appropriate design and analysis for this problem? Is it better than the design in part a?
 c. Explain how you would design a study to compare the effects of the two treatments on students’ performance in calculus class.
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