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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 7.1.16
7장, 문제 7.1.16

Stating Hypotheses In Exercises 11–16, the statement represents a claim. Write its complement and state which is H0 and which is Ha.


p = 0.21

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1
Identify the claim in the problem. The claim is that the population proportion is equal to 0.21, which can be written as p = 0.21.
Write the complement of the claim. The complement of 'p = 0.21' is 'p ≠ 0.21', as the complement represents all values not equal to 0.21.
Determine which statement is the null hypothesis (H₀). The null hypothesis always includes equality, so H₀: p = 0.21.
Determine which statement is the alternative hypothesis (Hₐ). The alternative hypothesis is the complement of the null hypothesis, so Hₐ: p ≠ 0.21.
Summarize the hypotheses: H₀: p = 0.21 (the claim) and Hₐ: p ≠ 0.21 (the complement).

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주요 개념

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

Hypothesis Testing

Hypothesis testing is a statistical method used to make decisions about a population based on sample data. It involves formulating two competing hypotheses: the null hypothesis (H0), which represents a statement of no effect or no difference, and the alternative hypothesis (Ha), which represents the claim being tested. The goal is to determine whether there is enough evidence to reject H0 in favor of Ha.
추천 영상:
가이드 코스
06:21
Step 1: Write Hypotheses

Null and Alternative Hypotheses

The null hypothesis (H0) is a statement that indicates no change or no effect, serving as a default position that there is no relationship between variables. The alternative hypothesis (Ha) is the statement that reflects the claim or effect that the researcher aims to support. In the context of the given question, H0 would state that the population proportion p is equal to 0.21, while Ha would state that p is not equal to 0.21.
추천 영상:
가이드 코스
06:21
Step 1: Write Hypotheses

Complement of a Hypothesis

The complement of a hypothesis refers to the opposite of the original statement. In hypothesis testing, if the null hypothesis states a specific value (e.g., p = 0.21), the complement would encompass all other possibilities (e.g., p ≠ 0.21). Understanding the complement is crucial for correctly formulating the alternative hypothesis and interpreting the results of the hypothesis test.
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교과서 질문

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교과서 질문

Stating Hypotheses In Exercises 11–16, the statement represents a claim. Write its complement and state which is H0 and which is Ha.


μ < 128

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교과서 질문

Hypothesis Testing Using Rejection Regions In Exercises 7–12, (a) identify the claim and state H0 and Ha, (b) find the critical value(s) and identify the rejection region(s), (c) find the standardized test statistic z, (d) decide whether to reject or fail to reject the null hypothesis, and (e) interpret the decision in the context of the original claim.


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P = 0.0838

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