A pvalue is a probability associated with your critical value. The critical value depends on the probability you are allowing for a Type I error. It measures the chance of getting results at least as strong as yours if the claim (H_{0}) were true.
The following figure shows the locations of a test statistic and their corresponding conclusions.
To find the pvalue for your test statistic:

Look up your test statistic on the appropriate distribution — in this case, on the standard normal (Z) distribution (see the following Ztables).

Find the probability that Z is beyond (more extreme than) your test statistic:

If H_{a} contains a lessthan alternative, find the probability that Z is less than your test statistic (that is, look up your test statistic on the Ztable and find its corresponding probability). This is the pvalue. (Note: In this case, your test statistic is usually negative.)

If H_{a} contains a greaterthan alternative, find the probability that Z is greater than your test statistic (look up your test statistic on the Ztable, find its corresponding probability, and subtract it from one). The result is your pvalue. (Note: In this case, your test statistic is usually positive.)

If H_{a} contains a notequalto alternative, find the probability that Z is beyond your test statistic and double it. There are two cases:
If your test statistic is negative, first find the probability that Z is less than your test statistic (look up your test statistic on the Ztable and find its corresponding probability). Then double this probability to get the pvalue.
If your test statistic is positive, first find the probability that Z is greater than your test statistic (look up your test statistic on the Ztable, find its corresponding probability, and subtract it from one). Then double this result to get the pvalue.

When testing H_{0}: p = 0.25 versus H_{a}: p < 0.25, you find that the pvalue of 1.25 by finding the probability that Z is less than 1.25. When you look this number up on the above Ztable, you find a probability of 0.1056 of Z being less than this value.
Note: If you had been testing the twosided alternative,
the pvalue would be 2 ∗ 0.1056, or 0.2112.
If the results are likely to have occurred under the claim, then you fail to reject H_{0} (like a jury decides not guilty). If the results are unlikely to have occurred under the claim, then you reject H_{0} (like a jury decides guilty).