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Questions and Answers
What is the consequence of rejecting a true null hypothesis?
What is the typical value of alpha (α) in hypothesis testing?
What is the effect of a larger sample size on Type I Error?
What is the result of a smaller significance level (α) in hypothesis testing?
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What is the definition of a Type I Error?
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How can Type I Error be minimized?
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What can be said about a one-to-one function?
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What is the inverse function of f denoted as?
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What is true about the domain and range of a one-to-one function?
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What is the purpose of the inverse function of f?
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What type of function has an inverse function?
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Study Notes
Hypothesis Testing: Type I Error
Definition: A Type I Error occurs when a true null hypothesis is rejected, resulting in a false positive.
Also known as:
- Alpha (α) error
- False positive error
Consequences:
- Rejection of a true null hypothesis can lead to incorrect conclusions and misguided decisions
- Resources may be wasted on pursuing a non-existent effect or relationship
- False claims can be made, damaging credibility and trust
Probability of Type I Error:
- Represented by the Greek letter alpha (α)
- Typically set to 0.05, indicating a 5% chance of rejecting a true null hypothesis
- The smaller the α, the lower the probability of a Type I Error, but the higher the probability of a Type II Error (failing to reject a false null hypothesis)
Factors affecting Type I Error:
- Sample size: Larger samples increase the likelihood of detecting a true effect, but also increase the risk of Type I Error
- Significance level (α): A smaller α reduces the risk of Type I Error, but increases the risk of Type II Error
- Test statistic and p-value: A p-value below α indicates a statistically significant result, but does not guarantee the absence of a Type I Error
Minimizing Type I Error:
- Use a conservative significance level (α) to reduce the risk of Type I Error
- Use multiple tests and replication to verify results
- Consider the consequences of a Type I Error and adjust the significance level accordingly
Type I Error
- Occurs when a true null hypothesis is rejected, resulting in a false positive
- Also known as Alpha (α) error or False positive error
Consequences of Type I Error
- Leads to incorrect conclusions and misguided decisions
- Wastes resources on pursuing a non-existent effect or relationship
- Damages credibility and trust with false claims
Probability of Type I Error
- Represented by the Greek letter alpha (α)
- Typically set to 0.05, indicating a 5% chance of rejecting a true null hypothesis
- A smaller α reduces the probability of Type I Error, but increases the probability of Type II Error
Factors Affecting Type I Error
- Larger samples increase the likelihood of detecting a true effect, but also increase the risk of Type I Error
- A smaller α reduces the risk of Type I Error, but increases the risk of Type II Error
- A p-value below α indicates a statistically significant result, but does not guarantee the absence of a Type I Error
Minimizing Type I Error
- Use a conservative significance level (α) to reduce the risk of Type I Error
- Use multiple tests and replication to verify results
- Consider the consequences of a Type I Error and adjust the significance level accordingly
Inverse Function of a One-to-One Function
- A one-to-one function, f, has a unique output (y) for each input (x) in its domain.
- For every y in the range of f, there is exactly one x in the domain of f that corresponds to it.
- The inverse function of f, denoted as f-1, is the correspondence from the range of f back to the domain of f.
- The inverse function f-1 reverses the direction of correspondence, taking each y in the range back to its unique corresponding x in the domain.
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Description
Understand the concept of Type I Error, also known as Alpha error or False positive error, in hypothesis testing, including its consequences and probability.