In Exercises 7–10, the statement represents a claim. Write its complement and state which is Ho and which is Ha.


σ=0.63

Verified step by step guidance

1. Understand the problem: The given statement is a claim about the population standard deviation (σ). The claim is that σ = 0.63. We need to write the complement of this claim and identify which statement is the null hypothesis (Ho) and which is the alternative hypothesis (Ha).
2. Recall the definitions: The null hypothesis (Ho) is a statement of no change, no effect, or equality. It is the hypothesis that we assume to be true unless there is strong evidence against it. The alternative hypothesis (Ha) is the statement that contradicts the null hypothesis and represents the claim we are testing.
3. Write the null hypothesis (Ho): Since the claim is that σ = 0.63, the null hypothesis will be Ho: σ = 0.63. This represents the assumption that the population standard deviation is equal to 0.63.
4. Write the alternative hypothesis (Ha): The complement of the claim is that σ ≠ 0.63. This represents the possibility that the population standard deviation is not equal to 0.63. Therefore, the alternative hypothesis is Ha: σ ≠ 0.63.
5. Summarize the hypotheses: The null hypothesis (Ho) is σ = 0.63, and the alternative hypothesis (Ha) is σ ≠ 0.63. These hypotheses will be used in hypothesis testing to determine whether there is sufficient evidence to reject the null hypothesis in favor of the alternative hypothesis.

Key Concepts

Null Hypothesis (Ho)

The null hypothesis, denoted as Ho, is a statement that indicates no effect or no difference in a statistical test. It serves as the default assumption that any observed effect is due to sampling variability. In this case, Ho would assert that the population standard deviation σ is equal to 0.63.

Alternative Hypothesis (Ha)

The alternative hypothesis, represented as Ha, is a statement that contradicts the null hypothesis. It suggests that there is an effect or a difference. For the given claim, Ha would state that the population standard deviation σ is not equal to 0.63, indicating a deviation from the null hypothesis.

Complement of a Hypothesis

The complement of a hypothesis refers to the opposite statement of the original claim. In hypothesis testing, if Ho states that σ equals a specific value, the complement would assert that σ does not equal that value. This is crucial for determining the scope of the test and understanding the relationship between Ho and Ha.