Two-tailed test

we want to know if $\overline{x}$ is significantly different from $\mu_0$ , in either direction.

confidence interval method: If the confidence interval for the population mean $\mu$ (cells B25 and B27) includes $\mu_0$ (the population mean when the null hypothesis is true), accept the null hypothesis. Otherwise, reject it (the appropriate conclusion appears in cell B28).

classic method: If the $t$ -statistic (cell B10) 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).