问一道题：NO.PZ201512020300000201

问题如下：

1. Batten wants to determine whether the sample correlation between the Stellar and CPIENG variables (-0.1452) is statistically significant. The critical value for the test statistic at the 0.05 level of significance is approximately 1.96. Batten should conclude that the statistical relationship between Stellar and CPIENG is:

选项：

significant, because the calculated test statistic has a lower absolute value than the critical value for the test statistic.

significant, because the calculated test statistic has a higher absolute value than the critical value for the test statistic.

not significant, because the calculated test statistic has a higher absolute value than the critical value for the test statistic.

解释：

B is correct.

because the calculated test statistic is

$t=\frac{r\sqrt{n-2}}{\sqrt{1-r^2}}=\frac{-0.1452\sqrt{248-2}}{\sqrt{1-{(-0.1452)}^2}}=-2.3017$

Because the absolute value of t = -2.3017 is greater than 1.96, the correlation coefficient is statistically significant. For a regression with one independent variable, the t-value (and significance) for the slope coefficient (which is -2.3014) should equal the t-value (and significance) of the correlation coefficient. The slight difference between these two t-values is caused by rounding error.