Stating the Null and Alternative Hypotheses In Exercises 25–30, write the claim as a mathematical statement. State the null and alternative hypotheses, and identify which represents the claim.


Tablets A tablet manufacturer claims that the mean life of the battery for a certain model of tablet is more than 8 hours.

Verified step by step guidance

1. Identify the claim: The manufacturer claims that the mean life of the battery for the tablet is more than 8 hours. This is a statement about the population mean (μ).
2. Express the claim mathematically: The claim can be written as μ > 8, where μ represents the mean battery life in hours.
3. Define the null hypothesis (H₀): The null hypothesis is the statement that there is no effect or no difference. It is the complement of the claim and includes equality. Thus, H₀: μ ≤ 8.
4. Define the alternative hypothesis (H₁): The alternative hypothesis is the statement that supports the claim. Since the claim is that the mean battery life is more than 8 hours, H₁: μ > 8.
5. Identify which hypothesis represents the claim: The claim is represented by the alternative hypothesis (H₁: μ > 8). The null hypothesis (H₀: μ ≤ 8) is tested against this claim.

Key Concepts

Null Hypothesis (H0)

The null hypothesis is a statement that indicates no effect or no difference, serving as a default position that there is no relationship between two measured phenomena. In this context, it would assert that the mean battery life of the tablet is 8 hours or less, providing a baseline for statistical testing.

Alternative Hypothesis (H1)

The alternative hypothesis is a statement that contradicts the null hypothesis, suggesting that there is an effect or a difference. For this scenario, it would claim that the mean battery life of the tablet is greater than 8 hours, representing the manufacturer's assertion and the focus of the statistical test.

Claim

A claim in hypothesis testing refers to the assertion made by the manufacturer that can be tested statistically. In this case, the claim is that the mean battery life exceeds 8 hours, which is represented by the alternative hypothesis, indicating the direction of the test and the expected outcome.