Reference no: EM131723618

Question: Recalling names of students. The Journal of Experimental Psychology-Applied (June 2000) published a study in which the ‘‘name game'' was used to help groups of students learn the names of other students in the group. The ‘‘name game'' requires the first student in the group to state his/her full name, the second student to say his/her name and the name of the first student, the third student to say his/her name and the names of the first two students, and so on. After making their introductions, the students listened to a seminar speaker for 30 minutes. At the end of the seminar, all students were asked to remember the full name of each of the other students in their group and the researchers measured the proportion of names recalled for each.

One goal of the study was to investigate the linear trend between y = recall proportion and x = position (order) of the student during the game. The data (simulated based on summary statistics provided in the research article) for 144 students in the first eight positions are saved in the NAMEGAME2 file. The first five and last five observations in the data set are listed in the table. [Note: Since the student in position 1 actually must recall the names of all the other students, he or she is assigned position number 9 in the data set.] Use the method of least squares to estimate the line, E(y) = β₀ + β₁x. Interpret the β estimates in the words of the problem.