6.1 Defining the p-value
To conduct a hypothesis test using the p-value, you calculate the test statistic, such as a z-score or t-score, and then use it to determine the corresponding p-value from a probability distribution table or statistical software.
The decision rules for using p-values are:
- If p-value ≤ α, you reject the null hypothesis.
- If p-value > α, you fail to reject the null hypothesis (accept the null hypothesis).
You can use graphs to illustrate this decision rule. For example, in a one-tailed test, the orange region indicates the area outside the pre-determining α levels in the graph shown in Figure 22.
If the p-value ≤ α (i.e. if the boundary of the shaded region falls inside the boundary of α), you will reject the null hypothesis.
If the p-value > α (i.e. if the vertical black line region is greater than the orange shaded region), you will not reject the null hypothesis.
As you can see from these illustrations, the p-value reflects the tail area of the normal distribution (the vertical blue line region is smaller than the orange-shaded region). Therefore, you can determine the exact p-value by calculating the z-score representing the boundary of the tail area of the normal distribution, and using the pre-determined z-score table to determine the area right of the z-score.
