A researcher collects information on students enrolled in a statistics course to determine if their level of anxiety changes from the time they begin the course to the time they end the course. Lower scores on the instrument reflect decreased anxiety toward statistics. The pretest and posttest scores for the students were: 88, 94, 91, 84, 80, 76, 96, 90, 83, 95. The posttest scores were: 56, 64, 72, 80, 42, 40, 51, 32, 61, 59. (The data are in respective order. For example, for student A the pretest score was 88 and posttest score was 56; for student B the pretest score was 94 and posttest score was 64, and so forth.) Conduct the appropriate statistical procedure at alpha of .05 to determine if there is a difference in statistics anxiety, on average, prior to and after completion of a statistics course. What is the confidence interval of the mean difference?
A) 4.68 to 14.79
B) 21.42 to 42.58
C) 53.42 to 74.58
D) 55.70 to 87.70

Question

Quizplus · Accepted Answer

The correct choice is to calculate the confidence interval of the mean difference between pretest and posttest scores. Given the significant decrease in scores from pretest to posttest, a paired samples t-test would be appropriate for analyzing the data. The confidence interval (CI) provides a range within which the true mean difference in anxiety levels before and after the course is expected to fall. The calculation of the CI involves the mean difference, the standard error of the difference, and the t-value for the given confidence level (95% in this case, with alpha = .05). The provided CI of 21.42 to 42.58 suggests a significant decrease in anxiety, indicating that the course effectively reduces statistics anxiety among students.

A Researcher Collects Information on Students Enrolled in a Statistics