Question 1200424: A group of investigators wishes to explore the relationship between the use of hair dyes and the development of breast cancer in females. A group of 1000 beauticians 40 - 49 years of age is identified and followed for five years. After five years, 20 new cases of breast cancer have occurred. Assume that breast cancer incidence over this time period for average American women in this age group is 7/1000. Test the hypothesis that using hair dyes increases the risk of breast cancer. Use ( =0.05).
Answer by textot(100)   (Show Source):
You can put this solution on YOUR website! This is for informational purposes only. For medical advice or diagnosis, consult a professional.
Here's how we can approach this hypothesis test:
**1. Define Hypotheses:**
* **Null Hypothesis (H0):** The incidence of breast cancer among beauticians is the same as the general population (7/1000).
* **Alternative Hypothesis (H1):** The incidence of breast cancer among beauticians is higher than the general population.
**2. Set Up the Test**
* We can use a chi-square test for this analysis.
**3. Calculate Expected Frequencies:**
* **Expected number of breast cancer cases:**
* Total beauticians * Expected incidence rate = 1000 * (7/1000) = 7 cases
**4. Create a Contingency Table:**
| | Breast Cancer | No Breast Cancer | Total |
|-------------|---------------|------------------|-------|
| Beauticians | 20 | 980 | 1000 |
| General Pop. | 7 | 993 | 1000 |
**5. Calculate the Chi-Square Statistic:**
* Use the following formula:
χ² = Σ [(Observed Frequency - Expected Frequency)² / Expected Frequency]
* Calculate for each cell in the table and sum them up.
**6. Determine Degrees of Freedom:**
* Degrees of Freedom (df) = (Rows - 1) * (Columns - 1) = (2 - 1) * (2 - 1) = 1
**7. Find the Critical Value:**
* Using a chi-square distribution table or a statistical software, find the critical value for α = 0.05 and df = 1.
* The critical valuefor α = 0.05 and df = 1 is 3.841.
**8. Compare Calculated Chi-Square to Critical Value:**
* If the calculated chi-square statistic is greater than the critical value, reject the null hypothesis.
**9. Make a Decision and Conclusion**
* **Based on the calculated chi-square value:**
* If χ² > 3.841, reject the null hypothesis. There is sufficient evidence at the 0.05 significance level to suggest that beauticians have a higher incidence of breast cancer than the general population.
* If χ² ≤ 3.841, fail to reject the null hypothesis. There is not sufficient evidence at the 0.05 significance level to suggest that beauticians have a higher incidence of breast cancer than the general population.
**Important Notes:**
* This is a simplified analysis.
* Real-world studies would need to consider various confounding factors, such as age, family history of breast cancer, lifestyle factors (smoking, alcohol consumption, etc.), and other relevant covariates.
* These results do not definitively prove causation.
* Further research is needed to establish a definitive link between hair dye use and breast cancer risk.
**Disclaimer:**
This information is for general knowledge and educational purposes only and does not constitute medical advice.
Let me know if you have any other questions or would like to explore a specific aspect in more detail.
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