19) Do a hypothesis for the following, make sure to include and label all five steps: Test the claim that Treatment is independent of your reaction. Use a .05 significance level. Drug Placebo Headaches 18 20 No Headaches 82 70
19) Do a hypothesis for the following, make sure to include and label all five steps: Test the claim that Treatment is independent of your reaction. Use a .05 significance level. Drug Placebo Headaches 18 20 No Headaches 82 70
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Can I get help with 19 please
![### Hypothesis Testing: Treatment Independence
**Objective**: To test the claim that treatment is independent of the reaction (occurrence of headaches).
**Significance Level**: 0.05
Given Data:
| | Drug | Placebo |
|-------------|------|---------|
| Headaches | 18 | 20 |
| No Headaches| 82 | 70 |
**Steps to be Included**:
1. **Formulate the Hypotheses**:
- Null Hypothesis (H0): Treatment is independent of the reaction (i.e., the treatment has no effect on the occurrence of headaches).
- Alternative Hypothesis (H1): Treatment is not independent of the reaction (i.e., the treatment has an effect on the occurrence of headaches).
2. **Determine the Test Statistic**:
- Use the Chi-Square test for independence.
- Calculate the expected frequencies for each cell in the contingency table.
3. **Calculate the Chi-Square Test Statistic**:
- Use the formula: χ² = Σ [(Observed - Expected)² / Expected].
- Compare the observed frequencies in the table to the expected frequencies assuming the null hypothesis is true.
4. **Determine the Critical Value and P-value**:
- Use a Chi-Square distribution table to find the critical value for α = 0.05 and degrees of freedom (df) = (rows - 1) * (columns - 1).
- Calculate the p-value associated with the test statistic.
5. **Make a Decision**:
- If the test statistic exceeds the critical value or if the p-value is less than 0.05, reject the null hypothesis.
- Otherwise, do not reject the null hypothesis.
**Visual Representation**:
There is a table representing the frequency of individuals experiencing headaches or no headaches after receiving either a drug or placebo:
- **Treatment Group (Drug)**:
- 18 individuals reported headaches.
- 82 individuals reported no headaches.
- **Control Group (Placebo)**:
- 20 individuals reported headaches.
- 70 individuals reported no headaches.
The table aids in calculating the expected frequencies and, subsequently, the Chi-Square test statistic.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff6ad1cd7-e883-4155-acb4-5513247aaa08%2F636828cb-3f39-4502-ab12-7227412fe00a%2Fmxb4t1_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Hypothesis Testing: Treatment Independence
**Objective**: To test the claim that treatment is independent of the reaction (occurrence of headaches).
**Significance Level**: 0.05
Given Data:
| | Drug | Placebo |
|-------------|------|---------|
| Headaches | 18 | 20 |
| No Headaches| 82 | 70 |
**Steps to be Included**:
1. **Formulate the Hypotheses**:
- Null Hypothesis (H0): Treatment is independent of the reaction (i.e., the treatment has no effect on the occurrence of headaches).
- Alternative Hypothesis (H1): Treatment is not independent of the reaction (i.e., the treatment has an effect on the occurrence of headaches).
2. **Determine the Test Statistic**:
- Use the Chi-Square test for independence.
- Calculate the expected frequencies for each cell in the contingency table.
3. **Calculate the Chi-Square Test Statistic**:
- Use the formula: χ² = Σ [(Observed - Expected)² / Expected].
- Compare the observed frequencies in the table to the expected frequencies assuming the null hypothesis is true.
4. **Determine the Critical Value and P-value**:
- Use a Chi-Square distribution table to find the critical value for α = 0.05 and degrees of freedom (df) = (rows - 1) * (columns - 1).
- Calculate the p-value associated with the test statistic.
5. **Make a Decision**:
- If the test statistic exceeds the critical value or if the p-value is less than 0.05, reject the null hypothesis.
- Otherwise, do not reject the null hypothesis.
**Visual Representation**:
There is a table representing the frequency of individuals experiencing headaches or no headaches after receiving either a drug or placebo:
- **Treatment Group (Drug)**:
- 18 individuals reported headaches.
- 82 individuals reported no headaches.
- **Control Group (Placebo)**:
- 20 individuals reported headaches.
- 70 individuals reported no headaches.
The table aids in calculating the expected frequencies and, subsequently, the Chi-Square test statistic.
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