Two-tailed test

we want to know if $\hat{p}$ is significantly different from $p_0$ , in either direction.

confidence interval method: If the confidence interval for the population proportion $p$ (cells B28 and B30) includes $p_0$ (the population proportion when the null hypothesis is true), accept the null hypothesis. Otherwise, reject it (the appropriate conclusion appears in cell B31).

classic method: If the $Z$ -score (cell B13) is less than $-z_{\alpha/2}$ or greater than $+z_{\alpha/2}$ , reject the null hypothesis. Otherwise, accept it (the appropriate conclusion appears in cell B22).

$P$ -value method: If the probability of obtaining a $Z$ -score 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 B25).