Skip to main content
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 7.1.48a
7장, 문제 7.1.48a

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?


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

검증된 단계별 안내
1
Step 1: Understand the problem. The claim states that 'at least 20% of renters are behind on rent payments in New Jersey.' This means the claim is about a population proportion (p) being at least 0.20. In hypothesis testing, the null hypothesis (H₀) typically represents the status quo or the claim being tested, while the alternative hypothesis (Hₐ) represents the complement or challenge to the null hypothesis.
Step 2: Define the null hypothesis (H₀). Since the claim is 'at least 20%,' this translates to H₀: p ≥ 0.20. The null hypothesis assumes that the proportion of renters behind on rent payments is at least 20%.
Step 3: Define the alternative hypothesis (Hₐ). The alternative hypothesis is the opposite of the null hypothesis. In this case, Hₐ: p < 0.20. This means the proportion of renters behind on rent payments is less than 20%.
Step 4: Interpret a decision to reject the null hypothesis. If the null hypothesis (H₀: p ≥ 0.20) is rejected, it means there is sufficient evidence to support the alternative hypothesis (Hₐ: p < 0.20). This suggests that the proportion of renters behind on rent payments is likely less than 20%.
Step 5: Interpret a decision to fail to reject the null hypothesis. If the null hypothesis is not rejected, it means there is not enough evidence to support the alternative hypothesis. In this case, we would conclude that the data does not provide sufficient evidence to suggest the proportion of renters behind on rent payments is less than 20%, and the claim that at least 20% are behind on rent payments cannot be ruled out.

비슷한 문제에 대한 검증된 영상 답변:

이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.
영상 길이:
2m
도움이 되었나요?

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 test this hypothesis against an alternative hypothesis to determine if there is enough evidence to reject it.
추천 영상:
06:21
Step 1: Write Hypotheses

Alternative Hypothesis

The alternative hypothesis (H1) represents a statement 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 are behind on rent payments. This hypothesis is what researchers seek to support through statistical evidence when conducting a hypothesis test.
추천 영상:
06:21
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. A decision to reject the null hypothesis indicates that the sample provides sufficient evidence to support the alternative hypothesis.
추천 영상:
06:21
Step 1: Write Hypotheses
관련 실천
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


a. you represent the Internet provider and want to support the claim?

43
views
교과서 질문

In Exercises 3–6, determine whether a normal sampling distribution can be used. If it can be used, test the claim.

Claim: p ≠0.15, α=0.05. Sample statistics: p_hat = 0.12, n=500

58
views
교과서 질문

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


a. t = 1.4


70
views
교과서 질문

A nutrition bar manufacturer claims that the standard deviation of the number of grams of carbohydrates in a bar is 1.11 grams. A random sample of 26 bars has a standard deviation of 1.19 grams. At α=0.05, is there enough evidence to reject the manufacturer’s claim? Assume the population is normally distributed.

68
views
교과서 질문

When you reject a true claim with a level of significance that is virtually zero, what can you infer about the randomness of your sampling process?

53
views
교과서 질문

A research center claims that more than 80% of U.S. adults think that mothers should have paid maternity leave. In a random sample of 50 U.S. adults, 82% think that mothers should have paid maternity leave. At α=0.05, is there enough evidence to support the center’s claim?

60
views