Textbook Question
Graphical Analysis In Exercises 9–12, state whether each standardized test statistic t allows you to reject the null hypothesis. Explain.
c. t = -2.096
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Ch. 7 - Hypothesis Testing with One Sample
Larson8th EditionElementary Statistics: Picturing the WorldISBN: 9780137493470
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Table of contents
- Ch. 1 - Introduction to Statistics87
- Ch. 2 - Descriptive Statistics176
- Ch. 3 - Probability184
- Ch. 4 - Discrete Probability Distributions102
- Ch. 5 - Normal Probability Distributions183
- Ch. 6 - Confidence Intervals154
- Ch. 7 - Hypothesis Testing with One Sample165
- Ch. 8 - Hypothesis Testing with Two Samples134
- Ch. 9 - Correlation and Regression87
- Ch. 10 - Chi-Square Tests and the F-Distribution87
Larson8th EditionElementary Statistics: Picturing the WorldISBN: 9780137493470Not the one you use?Change textbook
Chapter 7, Problem 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?
Verified step by step guidance1
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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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
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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06:21
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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06:21Step 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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06:21Step 1: Write Hypotheses
Related Practice
Textbook Question
Interpreting a Decision In Exercises 43–48, determine whether the claim represents the null hypothesis or the alternative hypothesis. If a hypothesis test is performed, how should you interpret a decision that
b. fails to reject the null hypothesis?
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Textbook Question
Graphical Analysis In Exercises 9–12, state whether each standardized test statistic t allows you to reject the null hypothesis. Explain.
b. t = 0
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Textbook Question
Interpreting a Decision In Exercises 43–48, determine whether the claim represents the null hypothesis or the alternative hypothesis. If a hypothesis test is performed, how should you interpret a decision that
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Textbook Question
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Textbook Question
Graphical Analysis In Exercises 9–12, state whether each standardized test statistic t allows you to reject the null hypothesis. Explain.
b. t = 1.42
58
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