Two-tailed hypothesis test; Why do we multiply p-value by two? I understand that in a two-tailed hypothesis test, we must multiply the p-value by two. i.e. if z=1.95 and it's a one-tailed hypothesis test, our p-value is 0.0256. But, if it's a two-tailed hypothesis test and z=1.95, we must multiply the p-value of 0.0256 by two. Hence, the correct p-value is 0.0512 for the two-tailed hypothesis test. I can draw it out on the standard normal curve and I understand that we must multiply the p-value by two. But, my question is **why** we have to multiply by two. What is the conceptual idea behind it?

$2$ because it is **two** -tailed.

The test is the probability of seeing that value or something more extreme if the null hypothesis is true. $2$ is more extreme than $1.95$; $-3$ is also more extreme.

So you want $\Pr(Z \ge 1.95)+\Pr(Z \le -1.95)$ which, by the symmetry of the normal distribution is equal to $2\times \Pr(Z \ge 1.95)$