Question 1177449: The yearly rates of traffic accidents and violations were studied for a group of 140 young adult males who volunteered for treatment for substance abuse.For the five years preceding treatment, their mean accident rate was 0.123 with a standard deviation of 0.167. At 05.0level of significance, test the claim that the sample differs from the general driving population with a mean accident rate of 0.075.Find the p-value for this test.
Answer by CPhill(1959)   (Show Source):
You can put this solution on YOUR website! **1. State the Hypotheses**
* Null Hypothesis (H0): The mean accident rate for the sample is equal to the general driving population mean (µ = 0.075)
* Alternative Hypothesis (H1): The mean accident rate for the sample is different from the general driving population mean (µ ≠ 0.075)
**2. Determine the Test Statistic**
Since we have a sample and the population standard deviation is unknown, we'll use a t-test. The test statistic is calculated as:
```
t = (x̄ - µ) / (s / √n)
```
Where:
* x̄ = sample mean (0.123)
* µ = hypothesized population mean (0.075)
* s = sample standard deviation (0.167)
* n = sample size (140)
Plugging in the values:
```
t = (0.123 - 0.075) / (0.167 / √140)
t ≈ 3.42
```
**3. Find the P-value**
Since the alternative hypothesis is µ ≠ 0.075 (a two-tailed test), we want the area in both tails of the t-distribution. We need to find the P-value associated with t = 3.42 with 139 degrees of freedom (df = n - 1 = 139).
Using a t-table or calculator, the P-value for a two-tailed test with t = 3.42 and df = 139 is approximately 0.0007.
**4. Compare P-value to Significance Level (α)**
* α = 0.05 (given)
* P-value (0.0007) < α (0.05)
**5. Decision**
Since the P-value is less than α, we reject the null hypothesis.
**6. Conclusion**
There is enough evidence at the 0.05 level of significance to support the claim that the mean accident rate for the sample of young adult males in substance abuse treatment differs from the general driving population.
**P-value:** The P-value for this test is approximately **0.0007**.
**Interpretation**
The results suggest that the mean accident rate for the group of young adult males in substance abuse treatment is significantly different from the general driving population's mean accident rate.
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