In a large clinical trial, 390,069 children were randomly assigned to two groups. The treatment group consisted of 193,173 children given a vaccine for a certain disease, and 40 of those children developed the disease. The other 196,896 children were given a placebo, and 128 of those children developed the disease. Consider the vaccine treatment group to be the first sample. Identify the values of n₁. P₁. 91, 02. P2. 92. P. and q. P₁ = (Type an integer or a decimal rounded to eight decimal places as needed.) 91₁ = (Type an integer or a decimal rounded to eight decimal places as needed.) 7₂ P₂ (Type an integer or a decimal rounded to eight decimal places as needed.) (Type an integer or a decimal rounded to eight decimal places as needed.) (Type an integer or a decimal rounded to eight decimal places as needed.) q= (Type an integer or a decimal rounded to eight decimal places as needed.)

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### Large Clinical Trial - Data Analysis

In a large clinical trial, 390,069 children were randomly assigned to two groups:

- **Treatment Group:** Consisted of 193,173 children who were given a vaccine for a certain disease. Out of these, 40 children developed the disease.

- **Placebo Group:** Consisted of 196,896 children who were given a placebo. Out of these, 128 children developed the disease.

Consider the vaccine treatment group to be the first sample. Identify the values of \( n_1, \hat{p_1}, \hat{q_1}, n_2, \hat{p_2}, \hat{q_2}, \hat{p}, \) and \( \hat{q} \).

#### Input the following values:

- \( n_1 = \) [    ]
  
- \( \hat{p_1} = \) [Type an integer or a decimal rounded to eight decimal places as needed.]
  
- \( \hat{q_1} = \) [Type an integer or a decimal rounded to eight decimal places as needed.]
    
- \( n_2 = \) [    ]

- \( \hat{p_2} = \) [Type an integer or a decimal rounded to eight decimal places as needed.]
    
- \( \hat{q_2} = \) [Type an integer or a decimal rounded to eight decimal places as needed.]
    
- \( \hat{p} = \) [Type an integer or a decimal rounded to eight decimal places as needed.]

- \( \hat{q} = \) [Type an integer or a decimal rounded to eight decimal places as needed.]

### Explanation of Variables:

- **\( n_1 \)**: Sample size of the treatment group.
- **\( \hat{p_1} \)**: Proportion of children in the treatment group who developed the disease.
- **\( \hat{q_1} \)**: Proportion of children in the treatment group who did not develop the disease.
- **\( n_2 \)**: Sample size of the placebo group.
- **\( \hat{p_2} \)**: Proportion of children in the placebo group who developed the disease.
- **\( \hat{q_2} \)**: Proportion of children in the placebo group who did not develop the disease.
- **\( \hat
Transcribed Image Text:### Large Clinical Trial - Data Analysis In a large clinical trial, 390,069 children were randomly assigned to two groups: - **Treatment Group:** Consisted of 193,173 children who were given a vaccine for a certain disease. Out of these, 40 children developed the disease. - **Placebo Group:** Consisted of 196,896 children who were given a placebo. Out of these, 128 children developed the disease. Consider the vaccine treatment group to be the first sample. Identify the values of \( n_1, \hat{p_1}, \hat{q_1}, n_2, \hat{p_2}, \hat{q_2}, \hat{p}, \) and \( \hat{q} \). #### Input the following values: - \( n_1 = \) [ ] - \( \hat{p_1} = \) [Type an integer or a decimal rounded to eight decimal places as needed.] - \( \hat{q_1} = \) [Type an integer or a decimal rounded to eight decimal places as needed.] - \( n_2 = \) [ ] - \( \hat{p_2} = \) [Type an integer or a decimal rounded to eight decimal places as needed.] - \( \hat{q_2} = \) [Type an integer or a decimal rounded to eight decimal places as needed.] - \( \hat{p} = \) [Type an integer or a decimal rounded to eight decimal places as needed.] - \( \hat{q} = \) [Type an integer or a decimal rounded to eight decimal places as needed.] ### Explanation of Variables: - **\( n_1 \)**: Sample size of the treatment group. - **\( \hat{p_1} \)**: Proportion of children in the treatment group who developed the disease. - **\( \hat{q_1} \)**: Proportion of children in the treatment group who did not develop the disease. - **\( n_2 \)**: Sample size of the placebo group. - **\( \hat{p_2} \)**: Proportion of children in the placebo group who developed the disease. - **\( \hat{q_2} \)**: Proportion of children in the placebo group who did not develop the disease. - **\( \hat
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