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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 7.1.60
7장, 문제 7.1.60

Graphical Analysis In Exercises 57–60, you are given a null hypothesis and three confidence intervals that represent three samplings. Determine whether each confidence interval indicates that you should reject H0. Explain your reasoning.
Graphical representation of null hypothesis and confidence intervals for statistical analysis.

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Step 1: Understand the null hypothesis (H0). The null hypothesis states that p ≥ 0.73, where p represents the population proportion. To reject H0, the confidence interval must not include values greater than or equal to 0.73.
Step 2: Analyze confidence interval (a). The interval is 0.73 < p < 0.75. Since this interval starts at 0.73 and includes values greater than 0.73, it does not provide evidence to reject H0.
Step 3: Analyze confidence interval (b). The interval is 0.715 < p < 0.725. This interval does not include 0.73 or any values greater than 0.73, which suggests that H0 can be rejected based on this sampling.
Step 4: Analyze confidence interval (c). The interval is 0.695 < p < 0.745. This interval includes 0.73, so it does not provide evidence to reject H0.
Step 5: Summarize the findings. Confidence interval (b) indicates rejection of H0 because it excludes 0.73 and values greater than 0.73, while intervals (a) and (c) do not provide evidence to reject H0 as they include values greater than or equal to 0.73.

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주요 개념

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

Null Hypothesis (H0)

The null hypothesis (H0) is a statement that there is no effect or no difference, and it serves as the default assumption in statistical testing. In this context, H0 states that the population proportion (p) is greater than or equal to 0.73. To determine whether to reject H0, we compare the confidence intervals from the samples to this hypothesis.
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06:21
Step 1: Write Hypotheses

Confidence Interval

A confidence interval is a range of values derived from sample data that is likely to contain the true population parameter. Each confidence interval provides an estimate of where the true proportion (p) lies. If a confidence interval does not include the value specified in the null hypothesis, it suggests that we may reject H0.
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06:33
Introduction to Confidence Intervals

Statistical Significance

Statistical significance refers to the likelihood that a result or relationship is caused by something other than mere random chance. In this scenario, if the confidence intervals for the sample proportions (p̂) do not overlap with the null hypothesis value (0.73), it indicates that the results are statistically significant, leading to a potential rejection of H0.
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05:53
Parameters vs. Statistics
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In Exercises 13–18, test the claim about the population mean μ at the level of significance α. Assume the population is normally distributed.

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교과서 질문

Graphical Analysis In Exercises 57–60, you are given a null hypothesis and three confidence intervals that represent three samplings. Determine whether each confidence interval indicates that you should reject H0. Explain your reasoning.

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Ha: μ ≤ 8.0

H0: μ > 8.0

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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.


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교과서 질문

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