Table of contents

1. Intro to Stats and Collecting Data55m
2. Describing Data with Tables and Graphs1h 55m
3. Describing Data Numerically1h 45m
4. Probability2h 16m
5. Binomial Distribution & Discrete Random Variables2h 33m
6. Normal Distribution and Continuous Random Variables1h 38m
7. Sampling Distributions & Confidence Intervals: Mean1h 53m
8. Sampling Distributions & Confidence Intervals: Proportion1h 12m
- Sampling Distribution of Sample Proportion
  29m
- Confidence Intervals for Population Proportion
  42m
9. Hypothesis Testing for One Sample2h 19m
10. Hypothesis Testing for Two Samples3h 26m
11. Correlation1h 6m
12. Regression1h 35m
13. Chi-Square Tests & Goodness of Fit1h 57m
14. ANOVA1h 0m

9. Hypothesis Testing for One Sample

Steps in Hypothesis Testing

Statistics

9. Hypothesis Testing for One Sample

Steps in Hypothesis Testing

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1:24 minutes

Problem 7.1.8

Textbook Question

True or False? In Exercises 5–10, determine whether the statement is true or false. If it is false, rewrite it as a true statement.

The level of significance is the maximum probability you allow for rejecting a null hypothesis when it is actually true.

Verified step by step guidance

Understand the concept of the level of significance: The level of significance, denoted as \( \alpha \), is the threshold probability set by the researcher to determine whether to reject the null hypothesis. It represents the maximum probability of making a Type I error, which occurs when the null hypothesis is rejected even though it is true.

Analyze the given statement: The statement claims that the level of significance is the maximum probability you allow for rejecting a null hypothesis when it is actually true. This aligns with the definition of \( \alpha \), as it is indeed the maximum probability of making a Type I error.

Determine if the statement is true or false: Based on the definition of the level of significance, the statement is true because it correctly describes \( \alpha \).

If the statement were false, rewrite it as a true statement: Since the statement is true, no rewriting is necessary. However, if it were false, you would need to clarify the definition of \( \alpha \) and its role in hypothesis testing.

Conclude the analysis: Confirm that the statement is true and explain why it aligns with the statistical concept of the level of significance.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Null Hypothesis

The null hypothesis is a fundamental concept in statistics that represents a default position or statement that there is no effect or no difference in a given situation. It serves as a baseline for statistical testing, where researchers aim to determine if there is enough evidence to reject this hypothesis in favor of an alternative hypothesis.

Level of Significance

The level of significance, often denoted as alpha (α), is the threshold probability set by researchers to determine whether to reject the null hypothesis. It represents the maximum acceptable risk of making a Type I error, which occurs when the null hypothesis is incorrectly rejected when it is true. Common levels of significance are 0.05, 0.01, and 0.10.

Type I Error

A Type I error occurs when a true null hypothesis is incorrectly rejected, leading to a false positive conclusion. This error is directly related to the level of significance; a lower alpha reduces the likelihood of a Type I error but may increase the risk of a Type II error, which is failing to reject a false null hypothesis.

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Textbook Question

What are the two types of hypotheses used in a hypothesis test? How are they related?

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Textbook Question

Does failing to reject the null hypothesis mean that the null hypothesis is true? Explain.

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Textbook Question

True or False? In Exercises 5–10, determine whether the statement is true or false. If it is false, rewrite it as a true statement.

In a hypothesis test, you assume the alternative hypothesis is true.

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Textbook Question

True or False? In Exercises 5–10, determine whether the statement is true or false. If it is false, rewrite it as a true statement.

A statistical hypothesis is a statement about a sample.

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Textbook Question

True or False? In Exercises 5–10, determine whether the statement is true or false. If it is false, rewrite it as a true statement.

A large P-value in a test will favor rejection of the null hypothesis.

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Textbook Question

True or False? In Exercises 5–10, determine whether the statement is true or false. If it is false, rewrite it as a true statement.

To support a claim, state it so that it becomes the null hypothesis.

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Textbook Question

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

σ^2 ≥ 1.2

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Textbook Question

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

p < 0.45

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True or False? In Exercises 5–10, determine whether the statement is true or false. If it is false, rewrite it as a true statement.The level of significance is the maximum probability you allow for rejecting a null hypothesis when it is actually true.

Key Concepts

Null Hypothesis

Level of Significance

Type I Error

Watch next

True or False? In Exercises 5–10, determine whether the statement is true or false. If it is false, rewrite it as a true statement.

The level of significance is the maximum probability you allow for rejecting a null hypothesis when it is actually true.