Ten pairs of points yielded a correlation coefficient $r$ of $0.790$. If $\alpha = 0.05$, which of the following statements is correct if $H _ { 0 } : \rho = 0$ ? (Do not calculate a $t$-value.)
A) Because 0.790 is greater than 0.602, the null hypothesis is not rejected.
B) There is no correlation between the variables.
C) Because 0.790 is greater than 0.632, the null hypothesis is rejected.
D) Because 0.790 is greater than 0.632, the null hypothesis is not rejected.

Question

Quizplus · Accepted Answer

The critical value for rejecting the null hypothesis depends on the significance level and the degrees of freedom (which, for correlation, is $n-2$, where $n$ is the number of pairs). Without calculating a $t$-value, if the correlation coefficient $r$ is greater than a critical value (which would be looked up in a table based on $\alpha$ and degrees of freedom), the null hypothesis ($\rho = 0$, indicating no correlation) is rejected. Since 0.790 is greater than 0.632, and assuming 0.632 is the critical value for $\alpha = 0.05$ with the appropriate degrees of freedom, we reject the null hypothesis, indicating there is statistically significant correlation.

Ten Pairs of Points Yielded a Correlation Coefficient rrr Of 0.7900.7900.790 If

Ten Pairs of Points Yielded a Correlation Coefficient $r$ Of $0.790$ If