Researchers conduct a study where subjects read a passage of text while listening to music. Roughly half of the subjects are randomly assigned to listen to music with lyrics, while the rest listen to music without lyrics. After reading, each subject takes a comprehension test. The researchers wish to test if the mean comprehension score for the group without lyrics is higher than those with lyrics. 1. Which of the following is the most appropriate test and alternative hypothesis?
A. Two-sample z-test with HA: μlyrics≠μwithoutμlyrics​​=μwithout​
B. Two-sample z-test with HA: μlyrics<μwithoutμlyrics​<μwit hout​
C. Two-sample t-test with HA: μlyrics≠μwithoutμlyrics​​=μwithout​
D. Two-sample t-test with HA: μlyrics<μwithoutμlyrics​<μwit hout​
E. Paired t-test with HA: μdiff≠0μdiff​​=0
F. Paired t-test with HA: μdiff>0μdiff​>0
2. Which of the following is the most reasonable approximation to the degrees of freedom?
a. 51
b. 49
c. 50
d. 48
e. 52
f. None of the above