SOLUTION: In a study, researchers wanted to measure the effect of alcohol on the hippocampal region, the portion of the brain responsible for long-term memory storage, in adolescents. TI res

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Question 1199826: In a study, researchers wanted to measure the effect of alcohol on the hippocampal region, the portion of the brain responsible for long-term memory storage, in adolescents. TI researchers randomly selected 23 adolescents with alcohol use disorders to determine whether the hippocampal volumes in the alcoholic adolescents were less than the norma volume of 8.78 cm°
An analysis of the sample data revealed that the hippocampal volume is approximately normal with no outliers and § = 7.72 cm
3 and s = 0.9 cm
3. Conduct
appropriate test at the a = 0.05 level of significance.
= Click the icon to view the table of critical t-values.
Answer by textot(100) (Show Source):
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**1. Set up Hypotheses**
* **Null Hypothesis (H₀):** μ ≥ 8.78 cm³ (Mean hippocampal volume in alcoholic adolescents is greater than or equal to the normal volume)
* **Alternative Hypothesis (H₁):** μ < 8.78 cm³ (Mean hippocampal volume in alcoholic adolescents is less than the normal volume)
**2. Calculate the Test Statistic**
* **t-statistic:**
* t = (x̄ - μ) / (s / √n)
* where:
* x̄ is the sample mean hippocampal volume
* μ is the hypothesized population mean (8.78 cm³)
* s is the sample standard deviation (0.9 cm³)
* n is the sample size (23)
* **Note:** Since the sample mean (x̄) is not provided, we cannot calculate the exact t-statistic.
**3. Determine the Critical Value**
* **Degrees of Freedom (df):** df = n - 1 = 23 - 1 = 22
* **Significance Level (α):** 0.05 (one-tailed test)
* **Critical Value:**
* Using a t-distribution table with 22 degrees of freedom and α = 0.05 (one-tailed), find the critical value.
* The critical value for a one-tailed test at α = 0.05 and df = 22 is approximately -1.717.
**4. Make a Decision**
* **Compare the Test Statistic to the Critical Value:**
* If the calculated t-statistic is less than the critical value (-1.717), we reject the null hypothesis.
**5. Conclusion**
* **If the calculated t-statistic is less than -1.717:**
* There is sufficient evidence at the 0.05 level of significance to conclude that the mean hippocampal volume in alcoholic adolescents is less than the normal volume of 8.78 cm³.
* **If the calculated t-statistic is greater than or equal to -1.717:**
* There is not enough evidence at the 0.05 level of significance to conclude that the mean hippocampal volume in alcoholic adolescents is less than the normal volume.
**Note:**
* This analysis requires the sample mean (x̄) of the hippocampal volumes for the 23 adolescents to calculate the t-statistic and make a definitive conclusion.
This approach provides the framework for conducting the hypothesis test. You would need the actual sample mean of hippocampal volumes to complete the analysis and draw a conclusion.