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


μ ≤ 375

Verified step by step guidance

1. Understand the claim: The claim is that the population mean (μ) is less than or equal to 375. This will help us determine the null hypothesis (H0) and the alternative hypothesis (Ha).
2. Write the complement of the claim: The complement of 'μ ≤ 375' is 'μ > 375'. This is because the complement of 'less than or equal to' is 'greater than'.
3. Identify the null hypothesis (H0): The null hypothesis always includes the equality part of the claim. Therefore, H0: μ ≤ 375.
4. Identify the alternative hypothesis (Ha): The alternative hypothesis is the complement of the null hypothesis. Therefore, Ha: μ > 375.
5. Summarize the hypotheses: H0: μ ≤ 375 (the claim), and Ha: μ > 375 (the complement). These hypotheses will be used for statistical testing.

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 case, H0 states that the population mean (μ) is less than or equal to 375, suggesting that any observed effect is due to sampling variability rather than a true effect.

Alternative Hypothesis (Ha)

The alternative hypothesis (Ha) represents the claim that contradicts the null hypothesis, indicating the presence of an effect or difference. For the given statement, Ha would be μ > 375, suggesting that the population mean is greater than 375, which is what the researcher aims to provide evidence for.

Complement of a Statement

The complement of a statement refers to the opposite of that statement. In hypothesis testing, if the null hypothesis is μ ≤ 375, its complement would be μ > 375. Understanding the complement is crucial for formulating the alternative hypothesis and interpreting the results of statistical tests.