Question 1193668: A study was to investigate the oral status of a group of patients diagnosed with thalassemia major (TM). One of the outcome measures was the decayed, missing, and filled teeth index (DMFT). In a sample of 18 patients the mean DMFT index value was 11.3 with a standard deviation of 6.3. Is this sufficient evidence to allow us to conclude that the mean DMFT index is greater than 9.0 in a population of similar subjects? Let alpha=5% (show all the steps)
Answer by proyaop(69)   (Show Source):
You can put this solution on YOUR website! **1. Set up Hypotheses**
* **Null Hypothesis (H0):** μ ≤ 9.0 (The population mean DMFT index is less than or equal to 9.0)
* **Alternative Hypothesis (H1):** μ > 9.0 (The population mean DMFT index is greater than 9.0)
**2. Calculate the t-statistic**
* t = (sample mean - population mean) / (sample standard deviation / √sample size)
* t = (11.3 - 9.0) / (6.3 / √18)
* t ≈ 1.549
**3. Determine Degrees of Freedom**
* Degrees of Freedom (df) = sample size - 1 = 18 - 1 = 17
**4. Find the Critical Value**
* Since this is a one-tailed test (we're only interested in whether the mean is *greater* than 9.0), we'll find the critical t-value for a one-tailed test with α = 0.05 and df = 17.
* Using a t-distribution table or statistical software, the critical t-value is approximately 1.740.
**5. Make a Decision**
* **Compare the calculated t-statistic to the critical t-value:**
* 1.549 < 1.740
* **Decision:** Since the calculated t-statistic (1.549) is less than the critical t-value (1.740), we **fail to reject the null hypothesis.**
**6. Conclusion**
* There is **not sufficient evidence** at the 0.05 level of significance to conclude that the mean DMFT index in the population of patients with thalassemia major is greater than 9.0.
**In summary:**
Based on the sample data, we cannot confidently conclude that the mean DMFT index for patients with thalassemia major is significantly higher than 9.0.
**Note:**
* This analysis assumes that the sample of patients is representative of the larger population of patients with thalassemia major.
* It also assumes that the DMFT index values in the population are normally distributed.
* If these assumptions are not met, the results of the t-test may not be reliable.
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