Music and memory Does listening to music while studying hinder students’ learning? Two AP® Statistics students designed an experiment to find out.

They selected a random sample of 30 students from their medium-sized high school to participate. Each subject was given 10 minutes to memorize two different lists of 20 words, once while listening to music and once in silence. The order of the two word lists was determined at random; so was the order of the treatments. The difference in the number of words recalled (music − silence) was recorded for each subject. A paired t test on the differences yielded t = −3.01 and P-value = 0.0027.

(a) State appropriate hypotheses for the paired t test. Be sure to define your parameter.

(b) What are the degrees of freedom for the paired t test?

(c) Interpret the P-value in context. What conclusion should the students draw?

(d) Describe a Type I error and a Type II error in this setting.

Which mistake could students have made based on your answer to part (c)?