2. The difference between the two groups has been declared statistically significant at the a = 0.05 level. Use the "No Adolescent Marijuana" group to determine a suitable p0, and then test the hypothesis: HO: p ≤ p0 HA: p > p0 where p is the population proportion (conceptualized) of all adolescent marijuana users who would develop schizophrenia. Show all your work. Are the results statistically significant as claimed? Make sure you report the standard score, a p-value, your conclusion, and a comment on what statistical risk has been taken and controlled for in this testing process.

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### Statistical Hypothesis Testing in Adolescent Marijuana Use and Schizophrenia 

#### Problem Statement

The difference in schizophrenia development between two groups has been declared statistically significant at the α = 0.05 level. Use the "No Adolescent Marijuana" group to determine a suitable \( p_0 \), and then test the hypothesis:

- \( H_0: p \leq p_0 \)
- \( H_A: p > p_0 \)

Where \( p \) is the population proportion (conceptualized) of all adolescent marijuana users who would develop schizophrenia. Show all your work. Are the results statistically significant as claimed? Make sure you report the standard score, a p-value, your conclusion, and a comment on what statistical risk has been taken and controlled for in this testing process.

#### Graph Explanation

The bar graph titled "A Particular COMT Gene and Psychosis" displays two groups:

- **No Adolescent Marijuana Use** (\( n = 311 \)): 2.3% of individuals developed schizophrenia.
- **Adolescent Marijuana Use** (\( n = 91 \)): 5.5% of individuals developed schizophrenia.

The graph visually represents the increased percentage of schizophrenia development in individuals with adolescent marijuana use compared to those with no use. This difference is the basis for the hypothesis testing.
Transcribed Image Text:### Statistical Hypothesis Testing in Adolescent Marijuana Use and Schizophrenia #### Problem Statement The difference in schizophrenia development between two groups has been declared statistically significant at the α = 0.05 level. Use the "No Adolescent Marijuana" group to determine a suitable \( p_0 \), and then test the hypothesis: - \( H_0: p \leq p_0 \) - \( H_A: p > p_0 \) Where \( p \) is the population proportion (conceptualized) of all adolescent marijuana users who would develop schizophrenia. Show all your work. Are the results statistically significant as claimed? Make sure you report the standard score, a p-value, your conclusion, and a comment on what statistical risk has been taken and controlled for in this testing process. #### Graph Explanation The bar graph titled "A Particular COMT Gene and Psychosis" displays two groups: - **No Adolescent Marijuana Use** (\( n = 311 \)): 2.3% of individuals developed schizophrenia. - **Adolescent Marijuana Use** (\( n = 91 \)): 5.5% of individuals developed schizophrenia. The graph visually represents the increased percentage of schizophrenia development in individuals with adolescent marijuana use compared to those with no use. This difference is the basis for the hypothesis testing.
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