Decision Making: P-value Method

The first step is stating and expressing a hypothesis symbolically. You formulate a claim about the population parameter based on your research question, then establish null and alternative hypotheses. The null hypothesis contains an equality symbol, while the alternative hypothesis may contain >, <, or ≠ symbols depending on the direction of your claim.

The significance level (α) is decided before calculating the test statistic. Common values are 0.05 or 0.01, corresponding to 95% or 99% confidence levels respectively. This predetermined threshold is used later to compare against the computed P-value to make your final decision about rejecting or failing to reject the null hypothesis.

When testing a population proportion, use the z statistic. The z statistic is also appropriate for testing the mean when the population standard deviation is known. For other scenarios, such as testing the mean with unknown population standard deviation, you would use a t statistic instead.

The P-value is the probability of obtaining a test statistic value at least as extreme as the one calculated from your sample data, assuming the null hypothesis is true. After computing your test statistic, you calculate or look up the corresponding P-value electronically or from a P-value table to compare it with your predetermined significance level.

If the computed P-value is equal to or smaller than the predetermined significance level (α), you reject the null hypothesis. If the P-value is larger than α, you fail to reject the null hypothesis. This comparison directly determines whether your sample data provides sufficient evidence to support the alternative hypothesis.

When testing a claim about the mean with an unknown population standard deviation, use the t statistic. For testing the variance or standard deviation itself, use the chi-square statistic. Selecting the correct test statistic depends on what population parameter you are testing and what information is available about the population.

The P-value method uses a calculated P-value to make a decision, while the traditional method uses critical values and a critical region. Both approaches lead to the same conclusion, but the P-value method directly compares the computed probability against the significance level, providing a more intuitive measure of evidence against the null hypothesis.