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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: 9780137493470Non è quello che usi tu?Cambia libro di testo
Tutti i libri di testoLarson 8th EditionCh. 7 - Hypothesis Testing with One SampleProblema 7.1.51b
Capitolo 7, Problema 7.1.51b

Writing Hypotheses: Backpack Manufacturer A backpack manufacturer claims that the mean life of its competitor’s backpacks is less than 5 years. You are asked to perform a hypothesis test to test this claim. How would you write the null and alternative hypotheses when


b. you represent the competitor and want to reject the claim?

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Step 1: Understand the context of the problem. The backpack manufacturer claims that the mean life of its competitor’s backpacks is less than 5 years. This is the alternative hypothesis (Hₐ) because it represents the claim being tested.
Step 2: Define the null hypothesis (H₀). The null hypothesis is the opposite of the alternative hypothesis and represents the status quo or no effect. In this case, H₀: μ ≥ 5, where μ is the mean life of the competitor’s backpacks.
Step 3: Define the alternative hypothesis (Hₐ). Since the manufacturer claims the mean life is less than 5 years, the alternative hypothesis is Hₐ: μ < 5.
Step 4: Represent the competitor and aim to reject the claim. To reject the claim, you would test the null hypothesis (H₀: μ ≥ 5) against the alternative hypothesis (Hₐ: μ < 5) using appropriate statistical methods.
Step 5: Choose the significance level (α) and perform the hypothesis test. Commonly, α = 0.05 is used. Based on the test results (e.g., p-value or test statistic), determine whether to reject H₀ or fail to reject H₀.

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Null Hypothesis (H0)

The null hypothesis is a statement that indicates no effect or no difference, serving as a default position in hypothesis testing. In this context, it would assert that the mean life of the competitor's backpacks is equal to or greater than 5 years, which is the claim being tested against.
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Step 1: Write Hypotheses

Alternative Hypothesis (H1)

The alternative hypothesis represents the statement that contradicts the null hypothesis, suggesting that there is an effect or a difference. For this scenario, if you want to reject the claim, the alternative hypothesis would state that the mean life of the competitor's backpacks is greater than 5 years.
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Step 1: Write Hypotheses

Hypothesis Testing

Hypothesis testing is a statistical method used to make inferences about population parameters based on sample data. It involves calculating a test statistic and comparing it to a critical value to determine whether to reject the null hypothesis in favor of the alternative hypothesis, thus providing evidence for or against the claim.
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Step 1: Write Hypotheses
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