Textbook Question
Graphical Analysis In Exercises 13 and 14, state whether each standardized test statistic X^2 allows you to reject the null hypothesis. Explain.
a. X^2=2.091
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 7.1.51a
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
a. you represent the manufacturer and want to support the claim?
Verified step by step guidance1
Understand the context: The manufacturer claims that the mean life of the competitor's backpacks is less than 5 years. This is a one-tailed hypothesis test because the claim is directional ('less than').
Define the null hypothesis (H₀): The null hypothesis always represents the status quo or no effect. In this case, it would state that the mean life of the competitor's backpacks is greater than or equal to 5 years. Mathematically, H₀: μ ≥ 5, where μ represents the mean life of the competitor's backpacks.
Define the alternative hypothesis (H₁): The alternative hypothesis represents the claim being tested. Since the manufacturer claims that the mean life is less than 5 years, the alternative hypothesis is H₁: μ < 5.
Verify the direction of the test: Since the alternative hypothesis uses '<', this is a left-tailed test. This will influence the critical region and p-value calculation during the hypothesis test.
Summarize the hypotheses: Null hypothesis (H₀): μ ≥ 5. Alternative hypothesis (H₁): μ < 5. These hypotheses will guide the statistical test to determine whether there is sufficient evidence to support the manufacturer's claim.
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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. This hypothesis is tested against the alternative hypothesis to determine if there is enough evidence to reject it.
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06:21
Step 1: Write Hypotheses
Alternative Hypothesis (H1)
The alternative hypothesis represents the claim or effect that the researcher aims to support. In this scenario, it would state that the mean life of the competitor's backpacks is less than 5 years. This hypothesis is what the manufacturer wants to prove, and it is accepted if the evidence from the data is strong enough to reject the null hypothesis.
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06:21Step 1: Write Hypotheses
Hypothesis Testing
Hypothesis testing is a statistical method used to make decisions about a population 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. The process includes setting significance levels, collecting data, and interpreting results to draw conclusions about the claims being tested.
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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?
Marketing A fitness equipment company claims that its competitor’s home gym does not have a customer satisfaction rate of 99%.
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?
Gas Mileage An automotive manufacturer claims that the standard deviation for the gas mileage of one of the vehicles it manufactures is 3.9 miles per gallon.
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
Textbook Question
Graphical Analysis In Exercises 9–12, state whether each standardized test statistic t allows you to reject the null hypothesis. Explain.
a. t = -1.755
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
a. rejects the null hypothesis?
Marketing A fitness equipment company claims that its competitor’s home gym does not have a customer satisfaction rate of 99%.