Two-tailed test

we want to know if $\overline{d}$ is significantly different from 0 , in either direction.

confidence interval method: If the confidence interval for the population mean difference $\mu_d$ (cells B18 and B20) includes 0 (the population mean difference when the null hypothesis is true), accept the null hypothesis. Otherwise, reject it (the appropriate conclusion appears in cell B22).

classic method: If the $t$ -statistic (cell B11) is less than $-t_{\alpha/2}$ or greater than $+t_{\alpha/2}$ , reject the null hypothesis. Otherwise, accept it (the appropriate conclusion appears in cell B19).

$P$ -value method: If the probability of obtaining a $t$ -statistic as large as the one in cell B10 or larger in absolute value is less than $\alpha$ , reject the null hypothesis. Otherwise, accept it (the appropriate conclusion appears in cell B22).