hypothesis always makes a precise statement about a number, never a range of numbers. This single number actually used in the null hypothesis may be based on available information about a relevant population, or it may be based on some existing standard or theory. The null hypothesis is also always makes a statement about a characteristic of the , never about a characteristic of the sample. In general, the alternative hypothesis asserts the opposite of the hypothesis and it species a range of values about the single number that appears in the null hypothesis. The alternative hypothesis is usually identied with the hypothesis, the informal hypothesis or hunch that, by implying the presence of something special in the underlying population, serves as inspiration for the entire investigation. A species precisely when He should be rejected. Decision rules are based on critical 2 scores that separate common from rare outcomes and dictate whether Ho should be retained or rejected. We can identify the proportion of the total area under the sampling distribution that is identied with rare outcomes. This proportion is often referred to as . The level of signicance indicates the degree of rarity among random outcomes required to reject the null hypothesis. The null hypothesis is rejected if the observed 2 value equals or exceeds the critical 2 value because it deviates too far into the tails of the sampling distribution. After a decision has been made to retain or reject the null hypothesis, the decision must be To summarize, the step by~step procedure for testing a hypothesis 1s: (1) state the research problem, (2) identify the statistical hypotheses, (3) specify a decision rule, (4) calculate the value of the observed 2, (5) make a decision, and (6) interpret the decision