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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: 9780137493470당신이 사용하는 게 아니라요?교과서 변경
모든 교과서Larson 8th EditionCh. 7 - Hypothesis Testing with One Sample문제 7.1.48b
7장, 문제 7.1.48b

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?


Rent A recent study claims that at least 20% of renters are behind on rent payments in New Jersey. 

검증된 단계별 안내
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Step 1: Understand the problem. The claim states that at least 20% of renters are behind on rent payments in New Jersey. This is a statistical hypothesis testing problem where we need to determine whether the claim represents the null hypothesis (H₀) or the alternative hypothesis (Hₐ).
Step 2: Define the null hypothesis (H₀) and the alternative hypothesis (Hₐ). The null hypothesis typically represents the status quo or the claim being tested. In this case, H₀: p ≥ 0.20, where p is the proportion of renters behind on rent payments. The alternative hypothesis (Hₐ) would be Hₐ: p < 0.20, as it challenges the claim.
Step 3: Interpret the decision to 'fail to reject the null hypothesis.' Failing to reject H₀ means that there is not enough statistical evidence to support the alternative hypothesis (Hₐ). In this context, it suggests that the data does not provide sufficient evidence to conclude that less than 20% of renters are behind on rent payments.
Step 4: Emphasize the importance of the decision. Failing to reject H₀ does not mean that H₀ is true; it simply means that the sample data does not provide strong enough evidence to reject it. The claim that at least 20% of renters are behind on rent payments remains plausible based on the data.
Step 5: Highlight the role of significance level (α). The decision to fail to reject H₀ depends on the chosen significance level (e.g., 0.05). If the p-value from the hypothesis test is greater than α, we fail to reject H₀. This step ensures that the interpretation aligns with the statistical framework used in the test.

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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Null Hypothesis

The null hypothesis (H0) 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 proportion of renters behind on payments is less than 20%. Researchers aim to gather evidence to either reject or fail to reject this hypothesis based on sample data.
추천 영상:
06:21
Step 1: Write Hypotheses

Alternative Hypothesis

The alternative hypothesis (H1) represents the claim that contradicts the null hypothesis, suggesting that there is an effect or a difference. In this case, it posits that at least 20% of renters in New Jersey are behind on rent payments. This hypothesis is what researchers seek to support through statistical testing.
추천 영상:
06:21
Step 1: Write Hypotheses

Failing to Reject the Null Hypothesis

Failing to reject the null hypothesis means that the evidence from the sample data is not strong enough to support the alternative hypothesis. It does not prove that the null hypothesis is true; rather, it indicates that there is insufficient evidence to conclude that at least 20% of renters are behind on payments. This decision can lead to further investigation or a reassessment of the data.
추천 영상:
06:21
Step 1: Write Hypotheses
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교과서 질문

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%.

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교과서 질문

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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교과서 질문

Graphical Analysis In Exercises 9–12, state whether each standardized test statistic t allows you to reject the null hypothesis. Explain.


c. t = 1.7


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교과서 질문

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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교과서 질문

Writing Hypotheses: Internet Provider An Internet provider is trying to gain advertising deals and claims that the mean time a customer spends online per day is greater than 28 minutes. You are asked to test this claim. How would you write the null and alternative hypotheses when


b. you represent a competing advertiser and want to reject the claim?

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교과서 질문

Graphical Analysis In Exercises 13 and 14, state whether each standardized test statistic X^2 allows you to reject the null hypothesis. Explain.


b. X^2=23.309

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