Decision Making: P-value Method

The P-value method uses a calculated P-value instead of the critical value to arrive at a decision about the hypothesis.

As a first step, a hypothesis is stated and expressed symbolically.

For testing the proportion, mean, or standard deviation of a population, the null and alternative hypotheses are expressed as follows.

As a next step, a significance level α is decided, which commonly is either 0.05 or 0.01.

Further, an appropriate test statistic is chosen and calculated using the sample data.

This test statistic is then used to compute the P-value directly.

The P-value is the probability of getting a test statistic value at least as extreme as the one obtained from sample data. We can plot a distribution that shows the given test statistic and P-value.

If the computed P-value is equal to or smaller than the decided significance level, we reject the null hypothesis; otherwise, we fail to reject the null hypothesis.