n Exercises 1–6, the statement represents a claim. Write its complement and state which is H0 and which is Ha.


p ≥ 0.64

Verified step by step guidance

1. Step 1: Understand the problem. The claim provided is 'p ≥ 0.64', where 'p' represents the population proportion. This is a hypothesis testing problem, and we need to identify the null hypothesis (H0) and the alternative hypothesis (Ha).
2. Step 2: Recall the definitions of H0 and Ha. The null hypothesis (H0) is a statement of no effect or no difference, and it always includes equality (e.g., '=', '≥', or '≤'). The alternative hypothesis (Ha) is the complement of H0 and represents what we are trying to find evidence for.
3. Step 3: Write the complement of the claim. The complement of 'p ≥ 0.64' is 'p < 0.64'. This is because the complement of 'greater than or equal to' is 'less than'.
4. Step 4: Assign H0 and Ha. Since the claim is 'p ≥ 0.64', this will be the null hypothesis (H0). The alternative hypothesis (Ha) will be the complement, which is 'p < 0.64'.
5. Step 5: Finalize the hypotheses. Write them as follows: H0: p ≥ 0.64 and Ha: p < 0.64. These hypotheses are now ready to be used in a hypothesis testing procedure.

Key Concepts

Null Hypothesis (H0)

The null hypothesis (H0) is a statement that indicates no effect or no difference, serving as a default position in statistical testing. In this context, it typically represents the status quo or a claim that a parameter, such as a population proportion, is equal to a specific value. For the given claim 'p ≥ 0.64', the null hypothesis would assert that 'p = 0.64'.

Alternative Hypothesis (Ha)

The alternative hypothesis (Ha) is a statement that contradicts the null hypothesis, suggesting that there is an effect or a difference. It represents the claim that researchers aim to support through statistical evidence. In this case, the alternative hypothesis would be 'p < 0.64', indicating that the population proportion is less than 0.64.

Complement of a Statement

The complement of a statement refers to the opposite scenario of the original claim. In hypothesis testing, the complement helps to define the alternative hypothesis. For the claim 'p ≥ 0.64', the complement would be 'p < 0.64', which is essential for determining the alternative hypothesis in this statistical context.