r 2 = 0.5329. The two-tailed 95% critical t for 24 df is 2.064. The calculated t is ~/24 x 0.5329/0.4671 = 5.2327, which is much larger than the critical t. The population correlation coefficient is in probability greater than zero. (Slight differences appearing in prior calculations based on these data are due to rounding.) Denote ps as the correlation coefficient of the population from which the sample was drawn. To test the null hypothesis H0: ps = 0.5, substitute the appropriate values in Eqs. (24.18) through

(24.21). m = 0.9287,/z = 0.5493, a = 0.2085, and z = 1.82. The critical z = 1.96. The calculated z is less; therefore, we must conclude that there is inadequate evidence to reject H0. The correlation has not been shown to be different from the theoretical value.