A researcher would like to conduct a hypothesis test to compare the mean SAT scores of students who have received extra coaching and the mean test score of students who have not received extra Coaching. He will randomly select 15 students and will use the difference between the student's
Score after coaching and the student's score before coaching as the paired-difference variable. He Obtains some normal probability plots of the sample data to determine whether it would be Reasonable to use a paired t-test. In which of the following situations would it be reasonable to use
A paired t-test ?
A: The distribution of the before test scores appears normal, the distribution of the after test scores
Appears normal, however the distribution of the paired differences does not appear normal.
B: The distribution of the before test scores is nonnormal, the distribution of the after test scores is
Nonnormal, however the distribution of the paired differences appears normal.
A) only
B)B only
C)A and B
D)Neither A nor B

Question

A researcher would like to conduct a hypothesis test to compare the mean SAT scores of students who have received extra coaching and the mean test score of students who have not received extra Coaching. He will randomly select 15 students and will use the difference between the student's
Score after coaching and the student's score before coaching as the paired-difference variable. He Obtains some normal probability plots of the sample data to determine whether it would be Reasonable to use a paired t-test. In which of the following situations would it be reasonable to use
A paired t-test ?
A: The distribution of the before test scores appears normal, the distribution of the after test scores
Appears normal, however the distribution of the paired differences does not appear normal.
B: The distribution of the before test scores is nonnormal, the distribution of the after test scores is
Nonnormal, however the distribution of the paired differences appears normal. 
A) only
B)B only
C)A and B
D)Neither A nor B

Quizplus · Accepted Answer

B)B onlyFor a paired t-test, the normality assumption applies to the distribution of the paired differences, not the distributions of the individual groups before and after the intervention. Therefore, it is reasonable to use a paired t-test when the distribution of the paired differences appears normal, even if the individual scores before and after coaching are not normally distributed.

A Researcher Would Like to Conduct a Hypothesis Test to Compare