## Podcast Beta

## 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.