K In a large clinical trial, 395,956 children were randomly assigned to two groups. The treatment group consisted of 198,649 children given a vaccine for a certain disease, and 27 of those children developed the disease. The other 197,307 children were given a placebo, and 107 of those children developed the disease. Consider the vaccine treatment group to be the first sample. Identify the values of n₁. P₁. ₁. ₂. P2, 92₂. P. and q.

MATLAB: An Introduction with Applications
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In a large clinical trial, 395,956 children were randomly assigned to two groups. The treatment group consisted of 198,649 children given a vaccine for a certain disease, and 27 of those children developed the disease. The other 197,307 children were given a placebo, and 107 of those children developed the disease. Consider the vaccine treatment group to be the first sample. Identify the values of \( n_1, p_1, q_1, n_2, p_2, q_2, \hat{p}, \) and \( \hat{q}. \)

\[ n_1 = \]

There is a blank space provided for entering the value of \( n_1 \). 

Explanation (for use on an educational website):

This text provides the context for solving a problem involving basic statistical calculations based on a clinical trial. The main goal is to understand the composition of two different groups in a medical study, where one group received a vaccine and the other a placebo. We are tasked with identifying various statistical parameters:

- \( n_1 \) and \( n_2 \) are the sample sizes for the treatment and placebo groups, respectively.
- \( p_1 \) and \( p_2 \) are the proportions of children who developed the disease in each group.
- \( q_1 \) and \( q_2 \) are the proportions of children who did not develop the disease in each group.
- \( \hat{p} \) is the overall proportion of children who developed the disease across both groups.
- \( \hat{q} \) is the overall proportion of children who did not develop the disease across both groups. 

The given numbers can be plugged into these equations to calculate the values and help understand the vaccine's effectiveness.
Transcribed Image Text:In a large clinical trial, 395,956 children were randomly assigned to two groups. The treatment group consisted of 198,649 children given a vaccine for a certain disease, and 27 of those children developed the disease. The other 197,307 children were given a placebo, and 107 of those children developed the disease. Consider the vaccine treatment group to be the first sample. Identify the values of \( n_1, p_1, q_1, n_2, p_2, q_2, \hat{p}, \) and \( \hat{q}. \) \[ n_1 = \] There is a blank space provided for entering the value of \( n_1 \). Explanation (for use on an educational website): This text provides the context for solving a problem involving basic statistical calculations based on a clinical trial. The main goal is to understand the composition of two different groups in a medical study, where one group received a vaccine and the other a placebo. We are tasked with identifying various statistical parameters: - \( n_1 \) and \( n_2 \) are the sample sizes for the treatment and placebo groups, respectively. - \( p_1 \) and \( p_2 \) are the proportions of children who developed the disease in each group. - \( q_1 \) and \( q_2 \) are the proportions of children who did not develop the disease in each group. - \( \hat{p} \) is the overall proportion of children who developed the disease across both groups. - \( \hat{q} \) is the overall proportion of children who did not develop the disease across both groups. The given numbers can be plugged into these equations to calculate the values and help understand the vaccine's effectiveness.
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