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

μ ≠ 150,020

검증된 단계별 안내

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.

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 >).

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.'

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.

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.

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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

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.

n Exercises 1–6, the statement represents a claim. Write its complement and state which is H0 and which is Ha.μ ≠ 150,020