The mean of the differences is 193 points, and the standard deviation of the differences is 62 point 7 3 points. The conditions for inference are met. A 98 percent confidence interval for the mean difference (after – before) in score is 137 point 0 4 points to 248 point 9 6 points. What is the correct interpretation of this interval?
Answer
A
98 percent of students in this sample increased their score, on average, by 137 point 0 4 to 248 point 9 6 points.
B
98 percent of students who take this course will increase their score, on average, by 137 point 0 4 to 248 point 9 6 points.
C
The school can be 98 percent confident that the students in the sample increased their SAT score, on average, by 137 point 0 4 to 248 point 9 6 points.
D
The school can be 98 percent confident that students who take this course increase their SAT score, on average, by 137 point 0 4 to 248 point 9 6 points.
Explanation
A confidence interval for the mean difference estimates the average score change for the population of students who take the course, not the change for each student or only for the sample. The school can be 98 percent confident that this population’s mean increase is between 137.04 and 248.96 points. Choice D gives that interpretation; the interval does not mean that 98 percent of students increased their scores by that amount.
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