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Ch. 7 - Hypothesis Testing with One Sample
Larson - Elementary Statistics: Picturing the World 8th Edition
Larson8th EditionElementary Statistics: Picturing the WorldISBN: 9780137493470Not the one you use?Change textbook
All textbooksLarson 8th EditionCh. 7 - Hypothesis Testing with One SampleProblem 7.1.11
Chapter 7, Problem 7.1.11

Stating Hypotheses In Exercises 11–16, the statement represents a claim. Write its complement and state which is H0 and which is Ha.


μ ≤ 645

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Step 1: Understand the problem. The given claim is μ ≤ 645, where μ represents the population mean. This is a one-tailed hypothesis test since it involves a 'less than or equal to' condition.
Step 2: Identify the null hypothesis (H0). The null hypothesis always includes the equality condition. Therefore, H0: μ ≤ 645.
Step 3: Write the complement of the claim. The complement of μ ≤ 645 is μ > 645. This represents the alternative hypothesis (Ha).
Step 4: Assign the hypotheses. Based on the claim and its complement, H0: μ ≤ 645 and Ha: μ > 645.
Step 5: Verify the setup. The null hypothesis (H0) is the statement of no effect or status quo, while the alternative hypothesis (Ha) is the statement we are testing for. Ensure the hypotheses are correctly assigned and aligned with the problem.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Hypothesis Testing

Hypothesis testing is a statistical method used to make decisions about a population based on sample data. It involves formulating two competing hypotheses: the null hypothesis (H0), which represents a statement of no effect or no difference, and the alternative hypothesis (Ha), which represents the claim being tested. The goal is to determine whether there is enough evidence to reject H0 in favor of Ha.
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Step 1: Write Hypotheses

Null and Alternative Hypotheses

The null hypothesis (H0) is a statement that indicates no change or effect, serving as a default position that there is no relationship between variables. In contrast, the alternative hypothesis (Ha) represents the claim that there is an effect or a difference. In the given example, H0 would be μ ≤ 645, while Ha would be μ > 645, indicating a claim that the population mean is greater than 645.
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Step 1: Write Hypotheses

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 certain condition, the complement would encompass all other possibilities. For the statement μ ≤ 645, the complement would be μ > 645, which is the alternative hypothesis that suggests the population mean exceeds 645.
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[Image]


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