Question
How to know to reject5or retain Ho
Answers
GPT-4o mini
To determine whether to reject or retain the null hypothesis (denoted as \( H_0 \)), you typically follow a structured hypothesis testing process. Here's a step-by-step guide:
### 1. Formulate the Hypotheses
- **Null Hypothesis (\( H_0 \))**: This is a statement of no effect or no difference that you aim to test against.
- **Alternative Hypothesis (\( H_a \))**: This is the statement that corresponds to your research question, indicating an effect or a difference.
### 2. Choose a Significance Level (\( \alpha \))
- Commonly used values for \( \alpha \) are 0.05, 0.01, or 0.10. This level represents the probability of rejecting the null hypothesis when it is true (Type I error).
### 3. Collect Data
- Gather the data necessary to perform the hypothesis test.
### 4. Select the Appropriate Statistical Test
- Choose the test that best fits your data and hypothesis (e.g., t-test, z-test, chi-square test, ANOVA, etc.).
### 5. Calculate the Test Statistic
- Use the selected statistical test to calculate the test statistic from your data.
### 6. Determine the Critical Value or P-value
- **Critical Value Method**: Compare the test statistic to a critical value from a statistical table based on \( \alpha \) and the test type (one-tailed or two-tailed).
- **P-value Method**: Calculate the p-value, which measures the probability of obtaining a test statistic at least as extreme as the one computed from your sample data, given that \( H_0 \) is true.
### 7. Make a Decision
- **Using Critical Value**: If the test statistic falls into the critical region (beyond the critical value), reject \( H_0 \). If it does not, retain \( H_0 \).
- **Using P-value**: If the p-value is less than or equal to \( \alpha \), reject \( H_0 \). If the p-value is greater than \( \alpha \), retain \( H_0 \).
### 8. Draw Conclusions
- State your conclusion in the context of the research question. If you reject \( H_0 \), do so with consideration of the potential implications and limitations of your analysis.
### Example
Let's say you're testing whether a new drug improves patient recovery time compared to a placebo.
1. **Hypotheses**:
- \( H_0 \): The drug has no effect on recovery time.
- \( H_a \): The drug improves recovery time.
2. **Significance Level**: Set \( \alpha = 0.05 \).
3. **Data Collection**: Gather data from clinical trials.
4. **Statistical Test**: You might choose a t-test if the data is normally distributed and you're comparing two means.
5. **Calculate Test Statistic**: Compute the t-statistic.
6. **Determine Critical Value**: Find the critical t-value for 0.05 (two-tailed) from a t-table based on your sample size.
7. **Decision**: If the t-statistic exceeds the critical value, reject \( H_0 \); if not, retain \( H_0 \).
8. **Conclusion**: Report whether the evidence supports the claim that the drug improves recovery time.
By following these steps, you can systematically decide whether to reject or retain the null hypothesis.
### 1. Formulate the Hypotheses
- **Null Hypothesis (\( H_0 \))**: This is a statement of no effect or no difference that you aim to test against.
- **Alternative Hypothesis (\( H_a \))**: This is the statement that corresponds to your research question, indicating an effect or a difference.
### 2. Choose a Significance Level (\( \alpha \))
- Commonly used values for \( \alpha \) are 0.05, 0.01, or 0.10. This level represents the probability of rejecting the null hypothesis when it is true (Type I error).
### 3. Collect Data
- Gather the data necessary to perform the hypothesis test.
### 4. Select the Appropriate Statistical Test
- Choose the test that best fits your data and hypothesis (e.g., t-test, z-test, chi-square test, ANOVA, etc.).
### 5. Calculate the Test Statistic
- Use the selected statistical test to calculate the test statistic from your data.
### 6. Determine the Critical Value or P-value
- **Critical Value Method**: Compare the test statistic to a critical value from a statistical table based on \( \alpha \) and the test type (one-tailed or two-tailed).
- **P-value Method**: Calculate the p-value, which measures the probability of obtaining a test statistic at least as extreme as the one computed from your sample data, given that \( H_0 \) is true.
### 7. Make a Decision
- **Using Critical Value**: If the test statistic falls into the critical region (beyond the critical value), reject \( H_0 \). If it does not, retain \( H_0 \).
- **Using P-value**: If the p-value is less than or equal to \( \alpha \), reject \( H_0 \). If the p-value is greater than \( \alpha \), retain \( H_0 \).
### 8. Draw Conclusions
- State your conclusion in the context of the research question. If you reject \( H_0 \), do so with consideration of the potential implications and limitations of your analysis.
### Example
Let's say you're testing whether a new drug improves patient recovery time compared to a placebo.
1. **Hypotheses**:
- \( H_0 \): The drug has no effect on recovery time.
- \( H_a \): The drug improves recovery time.
2. **Significance Level**: Set \( \alpha = 0.05 \).
3. **Data Collection**: Gather data from clinical trials.
4. **Statistical Test**: You might choose a t-test if the data is normally distributed and you're comparing two means.
5. **Calculate Test Statistic**: Compute the t-statistic.
6. **Determine Critical Value**: Find the critical t-value for 0.05 (two-tailed) from a t-table based on your sample size.
7. **Decision**: If the t-statistic exceeds the critical value, reject \( H_0 \); if not, retain \( H_0 \).
8. **Conclusion**: Report whether the evidence supports the claim that the drug improves recovery time.
By following these steps, you can systematically decide whether to reject or retain the null hypothesis.