Textbook Question
What are the two types of hypotheses used in a hypothesis test? How are they related?
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9. Hypothesis Testing for One Sample
Steps in Hypothesis Testing
1:24 minutesProblem 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.
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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.
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06:21
Step 1: Write Hypotheses
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.
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04:46Step 4: State Conclusion Example 4
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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