An educational psychologist conducts an experiment to determine whether varying the conditions in which learning and testing take place affects test results. She randomly selects 20 students who are unfamiliar with the Battle at Gettysburg from the Civil War. After presenting the material to the students and allowing them ample time to study, the students are given an exam. Ten of the students receive the lecture in a large lecture hall and 10 receive the lecture in a small classroom (both lectures have the same instructor). Of the students in the large lecture hall, five take the exam in the same large lecture hall, and five take the exam in a small classroom. Of the students in the small classroom, five take the exam in a large lecture hall and five take the exam in the same small classroom. The experimental design is, therefore, a \(2 \times 2\) factorial design with five replications in each cell. Table 15 gives the scores for each student.

Preliminary analysis indicates that the requirements for conducting a two-way ANOVA are satisfied. Test whether there is an interaction effect between the lecture location and exam location. Draw an interaction plot to confirm your results.
Approach We use StatCrunch to perform the two-way ANOVA and to draw the interaction plot.

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Table 15 Exam Given Large Lecture Hall Classroom Lecture Administered Large Lecture Hall Classroom 63 46 47 71 66 70 63 95 84 72 51 73 65 72 43 76 67 80 90 79