Chapter 9: Testing a Claim

The core structure involves formulating a null hypothesis representing no effect or no difference and an alternative hypothesis expressing the claim being tested, with the direction of the alternative hypothesis determining whether a one-sided or two-sided test is appropriate. Students learn to calculate a test statistic and its corresponding p-value, which quantifies the probability of observing data as extreme as or more extreme than what was actually obtained if the null hypothesis were true. The significance level, conventionally set at 0.05, serves as the decision threshold: if the p-value falls below this cutoff, the null hypothesis is rejected in favor of the alternative. A critical distinction emerges between Type I errors, which occur when a true null hypothesis is incorrectly rejected, and Type II errors, which occur when a false null hypothesis fails to be rejected. Statistical power, the complement of Type II error probability, measures the test's ability to detect a genuine effect. The chapter walks through practical applications for testing claims about population proportions and population means, emphasizing the importance of verifying conditions for inference before proceeding. Students learn to interpret p-values accurately within context, avoiding common misinterpretations that overstate evidence strength. Throughout, the chapter stresses both the utility of significance testing in making evidence-based decisions and its limitations, particularly regarding practical significance versus statistical significance and the dangers of misusing p-values in research.