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


μ≠2.28

Verified step by step guidance

1. Identify the claim in the problem. The claim is μ≠2.28, which is a statement about the population mean (μ). This indicates that the mean is not equal to 2.28.
2. Understand the complement of the claim. The complement of μ≠2.28 is μ=2.28, which states that the population mean is equal to 2.28.
3. Determine the null hypothesis (Ho). The null hypothesis always represents the statement of equality, so Ho: μ=2.28.
4. Determine the alternative hypothesis (Ha). The alternative hypothesis represents the claim being tested, so Ha: μ≠2.28.
5. Summarize the hypotheses: Ho: μ=2.28 (null hypothesis) and Ha: μ≠2.28 (alternative hypothesis). The alternative hypothesis is the claim, and the null hypothesis is its complement.

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, the null hypothesis would be that the population mean μ equals 2.28.

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 μ≠2.28, the alternative hypothesis would be that the population mean μ is not equal to 2.28, indicating a significant deviation from this value.

Complement of a Hypothesis

The complement of a hypothesis refers to the opposite scenario of the original claim. In hypothesis testing, if the null hypothesis states a specific value, the complement would encompass all other possibilities. For the claim μ≠2.28, the complement is μ=2.28, which is the condition under which the null hypothesis holds true.