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


p < 0.205

Verified step by step guidance

1. Identify the claim in the problem. The claim is 'p < 0.205', which is a statement about the population proportion (p).
2. Understand that the complement of the claim is the opposite of the inequality. The complement of 'p < 0.205' is 'p ≥ 0.205'.
3. Determine which statement represents the null hypothesis (H0) and which represents the alternative hypothesis (Ha). The null hypothesis (H0) always includes equality or '≥', while the alternative hypothesis (Ha) represents the claim or the inequality 'p < 0.205'.
4. Assign the hypotheses: H0: p ≥ 0.205 (the complement) and Ha: p < 0.205 (the claim).
5. Conclude that the null hypothesis (H0) is the statement to be tested, while the alternative hypothesis (Ha) is what we aim to support if the evidence is sufficient.

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 represents the claim that the population proportion is greater than or equal to 0.205, which is the opposite of the alternative hypothesis.

Alternative Hypothesis (Ha)

The alternative hypothesis (Ha) is a statement that contradicts the null hypothesis, suggesting that there is an effect or a difference. For the given claim 'p < 0.205', the alternative hypothesis would be that the population proportion is indeed less than 0.205, indicating a specific direction of interest.

Complement of a Statement

The complement of a statement refers to the opposite scenario of the original claim. In this case, the complement of 'p < 0.205' is 'p ≥ 0.205', which encompasses all values that are not less than 0.205, thus providing a complete view of the possible outcomes in hypothesis testing.