The researchers randomly selected 14 adolescents with alcohol use disorders to determine whether the hippocampal volumes in the alcoholic adolescents were less than 3 the normal volume of 9.02 cm An analysis of the sample data revealed that the 3 hippocampal volume is approximately normal with no outliers and x=8.09 cm³ and 3 s=0.8 cm. Conduct the appropriate test at the a= 0.01 level of significance. H₁ < 9.02 (Type integers or decimals. Do not round.) Identify the t-statistic. to = -4.35 (Round to two decimal places as needed.) Identify the P-value. P-value = (Round to three decimal places as needed.) an example Get more help. Clear all Check answer 2:00 PM

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### Study on the Effect of Alcohol on the Hippocampal Volume

In a study, researchers aimed to assess how alcohol consumption affects the hippocampal region, the brain area responsible for long-term memory storage in adolescents. The study involved randomly selecting 14 adolescents with alcohol use disorders to determine if their hippocampal volumes were less than the standard volume of 9.02 cm³.

**Sample Analysis:**
- The mean hippocampal volume from the sample: \( \bar{x} = 8.09 \, \text{cm}^3 \)
- Standard deviation: \( s = 0.8 \, \text{cm}^3 \)

**Hypothesis Testing:**
- Null Hypothesis (\( H_0 \)): \( \mu = 9.02 \)
- Alternative Hypothesis (\( H_1 \)): \( \mu < 9.02 \)

The statistical test is conducted at a \( \alpha = 0.01 \) level of significance.

**Calculation Details:**
- **T-Statistic:** 
  - Calculated as \( t_0 = -4.35 \) (rounded to two decimal places)
- **P-Value:** 
  - To be determined (round to three decimal places)

This analysis is instrumental in understanding whether alcohol use significantly affects brain structure in adolescents, specifically targeting potential reductions in hippocampal volume.
Transcribed Image Text:### Study on the Effect of Alcohol on the Hippocampal Volume In a study, researchers aimed to assess how alcohol consumption affects the hippocampal region, the brain area responsible for long-term memory storage in adolescents. The study involved randomly selecting 14 adolescents with alcohol use disorders to determine if their hippocampal volumes were less than the standard volume of 9.02 cm³. **Sample Analysis:** - The mean hippocampal volume from the sample: \( \bar{x} = 8.09 \, \text{cm}^3 \) - Standard deviation: \( s = 0.8 \, \text{cm}^3 \) **Hypothesis Testing:** - Null Hypothesis (\( H_0 \)): \( \mu = 9.02 \) - Alternative Hypothesis (\( H_1 \)): \( \mu < 9.02 \) The statistical test is conducted at a \( \alpha = 0.01 \) level of significance. **Calculation Details:** - **T-Statistic:** - Calculated as \( t_0 = -4.35 \) (rounded to two decimal places) - **P-Value:** - To be determined (round to three decimal places) This analysis is instrumental in understanding whether alcohol use significantly affects brain structure in adolescents, specifically targeting potential reductions in hippocampal volume.
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