Decision Making: Traditional Method

The traditional method involves stating null and alternative hypotheses symbolically, obtaining a critical value at a predetermined significance level, calculating a test statistic from sample data, and plotting both on a probability distribution. The null hypothesis is rejected if the test statistic falls within the critical region; otherwise, you fail to reject it.

Null and alternative hypotheses are expressed symbolically based on the population parameter being tested. By convention, the null hypothesis contains an equality symbol, while the alternative hypothesis contains >, <, or ≠ symbols. The null hypothesis represents a neutral statement, while the alternative hypothesis may have a specific direction or represent the original research claim.

When the population standard deviation is unknown, use the t statistic to test a claim about a population mean. The t statistic is calculated from sample data and compared against the critical value obtained from the t distribution at your chosen significance level.

Common significance levels follow a general convention of 95% confidence (α = 0.05) or 99% confidence (α = 0.01). The significance level determines the critical value and defines the critical region boundaries on the probability distribution where you reject the null hypothesis.

Compare your calculated test statistic to the critical region on the probability distribution. If the test statistic falls within the critical region, reject the null hypothesis. If it falls outside the critical region, fail to reject the null hypothesis. This decision does not require calculating the p-value.

The z statistic tests claims about proportions or means when population standard deviation is known. The t statistic tests claims about means when population standard deviation is unknown. The chi-square statistic tests claims about population variance or standard deviation. Each uses its respective distribution to determine critical values.

The critical value demarcates the critical region on the probability distribution at your chosen significance level. It serves as the boundary for decision-making: if your test statistic exceeds this boundary, you reject the null hypothesis. Critical values are obtained from z, t, or chi-square tables depending on your test statistic type.