Refer to the Journal of Experimental Psychology-Applied (June 2000) study in which the "name game" was used to help groups of students learn the names of other students in the group, Recall that one goal of the study was to investigate the relationship between proportion y of names recalled by a student and position (order x ) of the student during the game. The data 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 below.) A SAS printout follows.
Position Recall
2 .............. 0.04
2.............. 0.37
2.............. 1.00
2 .............. 0.99
2.............. 0.79
. .............. .
. .............. .
. .............. .
9................ 0.72
9................ 0.88
9 ................ 0.46
9 ................ 0.54
9 ................ 0.99

a. To properly apply the parametric test for correlation on the basis of the Pearson coefficient of correlation, r (Section 11.6) both the x and y variables must be normally distributed. Demonstrate that this assumption is violated for these data. What are the consequences of the violation?
b. Find Spearman's rank correlation coefficient on the accompanying SAS printout and interpret its value.
c. Find the observed significance level for testing for zero rank correlation on the SAS printout, and interpret its value.
d. At α = .05, is there sufficient evidence of rank correlation between proportion y of names recalled by a student and position (order x) of the student during the game?

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The CORR Procedure 2 Variables: POSITION RECALL Spearnan Correlation Coefficients, N144 Prob t under HO: Rho-0 POSITION 1.00000 RECALL POSITION 0.20652 0.0130 0.20652 0.0130 RECALL 1.00000