Final answer:
In hypothesis testing, the null hypothesis (H0) represents a statement of no effect or no difference, using equality symbols, while the alternative hypothesis (Ha or H1) indicates the possible effect or difference, using inequality symbols. The test can be right-tailed, left-tailed, or two-tailed, depending on the direction of the inequality.
Step-by-step explanation:
Formulating Null and Alternative Hypotheses in Hypothesis Testing
In hypothesis testing, the first step is to create two competing hypotheses: the null hypothesis (H0) and the alternative hypothesis (Ha or H1). The null hypothesis represents a statement of no effect or no difference, and it is the hypothesis that is assumed to be true unless evidence suggests otherwise. It is formulated using symbols of equality (e.g., =, ≤, or ≥). For example, if we're testing a new drug's effectiveness, the null hypothesis could be that the mean effectiveness of the new drug is equal to the mean effectiveness of the current standard drug.
The alternative hypothesis, on the other hand, is a statement that indicates the presence of an effect or difference. It is where we articulate what we suspect may be true instead of the null hypothesis and is denoted using symbols of inequality (e.g., ≠, >, or <). Continuing with the drug example, the alternative hypothesis might be that the new drug has greater effectiveness than the standard drug.
Whether a hypothesis test is right-tailed, left-tailed, or two-tailed is determined by the direction of the inequality in the alternative hypothesis. A right-tailed test is used when the alternative hypothesis has a greater than sign (>), a left-tailed test for a less than sign (<), and a two-tailed test for a not equal to sign (≠).