Throughout this textbook we use the classical methods of evaluating statistical hypothesis testing; however many computer programs instead of computing the test-statistics like z and t, gives a probability instead.

This probability is called the p-value and it is the probability of the test statistics.
 

P-value approach to hypothesis testing: The p-value is the probability of getting the test statistics in support of the alternate hypothesis. If p is the p-value: When testing the hypothesis at a level of significance, alpha, we reject the null hypothesis if: We do not reject the null hypothesis is

The p-value gives the degree of the failure of the test to accept the null hypothesis.

Example a p-value of 0.0001 compared to a p-value of 0.002 suggest that in the first case the failure to meet a alpha of 0.025 is worse than the second case.

Example: For a normal random variable of mean = 150 and standard deviation of 10, when comparing the value of a new mean of 165 for a large sample size, gives a p-value of 0.0668.

This p-value of 0.0668 > 0.05 , and if alpha of 0.05 is the level of significance, we would not reject the null hypothesis, that 150 = 165.

Be alert for p-values and know the rules in interpreting them.