A p-value 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 (H0) were true.
The following figure shows the locations of a test statistic and their corresponding conclusions.

To find the p-value for your test statistic:
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Look up your test statistic on the appropriate distribution — in this case, on the standard normal (Z-) distribution (see the following Z-tables).
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Find the probability that Z is beyond (more extreme than) your test statistic:
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If Ha contains a less-than alternative, find the probability that Z is less than your test statistic (that is, look up your test statistic on the Z-table and find its corresponding probability). This is the p-value. (Note: In this case, your test statistic is usually negative.)
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If Ha contains a greater-than alternative, find the probability that Z is greater than your test statistic (look up your test statistic on the Z-table, find its corresponding probability, and subtract it from one). The result is your p-value. (Note: In this case, your test statistic is usually positive.)
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If Ha contains a not-equal-to 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 Z-table and find its corresponding probability). Then double this probability to get the p-value.
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 Z-table, find its corresponding probability, and subtract it from one). Then double this result to get the p-value.
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These calculations give you a test statistic (standard score) of –0.05 divided by 0.04 = –1.25. This tells you that your sample results and the population claim in H0 are 1.25 standard errors apart; in particular, your sample results are 1.25 standard errors below the claim.
When testing H0: p = 0.25 versus Ha: p < 0.25, you find that the p-value of -1.25 by finding the probability that Z is less than -1.25. When you look this number up on the above Z-table, you find a probability of 0.1056 of Z being less than this value.
Note: If you had been testing the two-sided alternative,

the p-value would be 2 ∗ 0.1056, or 0.2112.
If the results are likely to have occurred under the claim, then you fail to reject H0 (like a jury decides not guilty). If the results are unlikely to have occurred under the claim, then you reject H0 (like a jury decides guilty).