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those In a large clinical trial, 393,820 children were randomly assigned to two groups. The treatment group consisted of 195,281 children given a vaccine for a certain disease, and 25 of children developed the disease. The other 198,539 children were given a placebo, and 89 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. A Inc

those In a large clinical trial, 393,820 children were randomly assigned to two groups. The treatment group consisted of 195,281 children given a vaccine for a certain disease, and 25 of children developed the disease. The other 198,539 children were given a placebo, and 89 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. A Inc

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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**Clinical Trial Analysis** In a large clinical trial, 393,820 children were randomly assigned to two groups. The treatment group consisted of 195,281 children given a vaccine for a certain disease, and 25 of those children developed the disease. The other 198,539 children were given a placebo, and 89 of those children developed the disease. Consider the vaccine treatment group to be the first sample. Identify the values of \(n_1\), \(p_1\), \(q_1\), \(n_2\), \(p_2\), \(q_2\), \(p\), and \(\hat{q}\). ### Values - \( n_1 \) = - \( p_1 \) = - \( q_1 \) = - \( n_2 \) = - \( p_2 \) = - \( q_2 \) = - \( p \) = - \( \hat{q} \) = <Graphical details: There is no graphical content within the provided image.> ### Explanation: - **\( n_1 \)**: Number of children in the treatment group (vaccine). - **\( p_1 \)**: Proportion of children who developed the disease in the treatment group. - **\( q_1 \)**: Proportion of children who did not develop the disease in the treatment group. - **\( n_2 \)**: Number of children in the placebo group. - **\( p_2 \)**: Proportion of children who developed the disease in the placebo group. - **\( q_2 \)**: Proportion of children who did not develop the disease in the placebo group. - **\( p \)**: Combined proportion of children who developed the disease in both groups. - **\( \hat{q} \)**: Predicted proportion of children who did not develop the disease. The image also includes a text entry box beneath where \(n_1\) is indicated, implying the requirement to input specific values as part of an exercise. The function buttons such as "Help me solve this," "View an example," "Get more help," "Clear all," and "Check answer" suggest an interactive learning module.
Transcribed Image Text:**Clinical Trial Analysis** In a large clinical trial, 393,820 children were randomly assigned to two groups. The treatment group consisted of 195,281 children given a vaccine for a certain disease, and 25 of those children developed the disease. The other 198,539 children were given a placebo, and 89 of those children developed the disease. Consider the vaccine treatment group to be the first sample. Identify the values of \(n_1\), \(p_1\), \(q_1\), \(n_2\), \(p_2\), \(q_2\), \(p\), and \(\hat{q}\). ### Values - \( n_1 \) = - \( p_1 \) = - \( q_1 \) = - \( n_2 \) = - \( p_2 \) = - \( q_2 \) = - \( p \) = - \( \hat{q} \) = <Graphical details: There is no graphical content within the provided image.> ### Explanation: - **\( n_1 \)**: Number of children in the treatment group (vaccine). - **\( p_1 \)**: Proportion of children who developed the disease in the treatment group. - **\( q_1 \)**: Proportion of children who did not develop the disease in the treatment group. - **\( n_2 \)**: Number of children in the placebo group. - **\( p_2 \)**: Proportion of children who developed the disease in the placebo group. - **\( q_2 \)**: Proportion of children who did not develop the disease in the placebo group. - **\( p \)**: Combined proportion of children who developed the disease in both groups. - **\( \hat{q} \)**: Predicted proportion of children who did not develop the disease. The image also includes a text entry box beneath where \(n_1\) is indicated, implying the requirement to input specific values as part of an exercise. The function buttons such as "Help me solve this," "View an example," "Get more help," "Clear all," and "Check answer" suggest an interactive learning module.
Below is what appears in the provided image. This content is related to statistical notation and estimation. --- \( n_1 = \) \( \hat{p_1} = \) (Type = \( \hat{q_1} = \) (Type = \( n_2 = \) \( \hat{p_2} = \) (Type = \( \hat{q_2} = \) (Type = \( \overline{p} = \) (Type = \( \overline{q} = \) (Type = --- Explanation: - \(n_1\): Likely represents the sample size for the first group or population. - \(\hat{p_1}\): Represents the estimated proportion for the first sample. - \(\hat{q_1}\): Represents the complement of \(\hat{p_1}\) (i.e., \(\hat{q_1} = 1 - \hat{p_1}\)), indicating the proportion not in the first category. - \(n_2\): Likely represents the sample size for the second group or population. - \(\hat{p_2}\): Represents the estimated proportion for the second sample. - \(\hat{q_2}\): Represents the complement of \(\hat{p_2}\) (i.e., \(\hat{q_2} = 1 - \hat{p_2}\)), indicating the proportion not in the second category. - \(\overline{p}\): Represents the combined proportion, a pooled estimate from both samples. - \(\overline{q}\): Represents the complement of \(\overline{p}\) (i.e., \(\overline{q} = 1 - \overline{p}\)), indicating the pooled proportion not in the combined category. Each of these notations are followed by the indication "(Type = " which usually implies that they could be variables where different types of data can be inputted or derived in a statistical software or context.
Transcribed Image Text:Below is what appears in the provided image. This content is related to statistical notation and estimation. --- \( n_1 = \) \( \hat{p_1} = \) (Type = \( \hat{q_1} = \) (Type = \( n_2 = \) \( \hat{p_2} = \) (Type = \( \hat{q_2} = \) (Type = \( \overline{p} = \) (Type = \( \overline{q} = \) (Type = --- Explanation: - \(n_1\): Likely represents the sample size for the first group or population. - \(\hat{p_1}\): Represents the estimated proportion for the first sample. - \(\hat{q_1}\): Represents the complement of \(\hat{p_1}\) (i.e., \(\hat{q_1} = 1 - \hat{p_1}\)), indicating the proportion not in the first category. - \(n_2\): Likely represents the sample size for the second group or population. - \(\hat{p_2}\): Represents the estimated proportion for the second sample. - \(\hat{q_2}\): Represents the complement of \(\hat{p_2}\) (i.e., \(\hat{q_2} = 1 - \hat{p_2}\)), indicating the proportion not in the second category. - \(\overline{p}\): Represents the combined proportion, a pooled estimate from both samples. - \(\overline{q}\): Represents the complement of \(\overline{p}\) (i.e., \(\overline{q} = 1 - \overline{p}\)), indicating the pooled proportion not in the combined category. Each of these notations are followed by the indication "(Type = " which usually implies that they could be variables where different types of data can be inputted or derived in a statistical software or context.
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