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


μ ≠ 150,020

Verified step by step guidance

1. Step 1: Understand the problem. The given claim is μ ≠ 150,020, which is a statement about the population mean (μ). This is a two-tailed claim because it states that μ is not equal to a specific value.
2. Step 2: Recall the definitions of null hypothesis (H0) and alternative hypothesis (Ha). The null hypothesis (H0) is a statement of no effect or no difference, and it typically includes equality (e.g., =, ≤, or ≥). The alternative hypothesis (Ha) is the claim being tested and represents a statement of inequality (e.g., ≠, <, or >).
3. Step 3: Write the complement of the claim. The complement of μ ≠ 150,020 is μ = 150,020. This is because the complement of 'not equal to' is 'equal to.'
4. Step 4: Assign H0 and Ha. The null hypothesis (H0) will be the complement of the claim, so H0: μ = 150,020. The alternative hypothesis (Ha) will be the original claim, so Ha: μ ≠ 150,020.
5. Step 5: Summarize the hypotheses. The null hypothesis (H0) is μ = 150,020, and the alternative hypothesis (Ha) is μ ≠ 150,020. These hypotheses will be used in hypothesis testing to determine whether there is enough evidence to reject H0 in favor of Ha.

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 asserts that the population mean (μ) is equal to a specific value, which is 150,020. Researchers aim to gather evidence against H0 to support an alternative hypothesis.

Alternative Hypothesis (Ha)

The alternative hypothesis (Ha) represents a statement that contradicts the null hypothesis, suggesting that there is an effect or a difference. In this case, Ha is that the population mean (μ) is not equal to 150,020, indicating a significant deviation from this value. It is what researchers hope to support through their data analysis.

Complement of a Statement

The complement of a statement refers to the opposite of that statement. For the claim μ ≠ 150,020, the complement would be μ = 150,020. Understanding complements is crucial in hypothesis testing, as it helps clarify the relationship between the null and alternative hypotheses, ensuring a comprehensive approach to statistical analysis.