9.11. Let XI = arithmetic speed, x 2 = arithmetic power, x) = intellectual interest.

x 4 = soeal interest, x5 = activity interest. Kelley (1928) observed the following correlations between batteries of tests identified as above, based on 109 pupils:

Let Xl\)' =(xl.x2) and x(2 ), = (X3,x4,XS)' Test the hypothesis that x(1) is independent of x(2) at the 1 % significance level.

0.4249 1.0000 0.4249 -0.0552 -0.0031 1.0000 -0.0416 0.1927 0.0495 0.0687 -0.0552 -0.0416 1.0000 0.7474 0.1691 -0.0031 0.0495 0.7474 1.0000 0.2653 0.1927 0.0687 0.1691 0.2653 1.0000,