Pew Research Center survey asked a variety of science questions of independent rande public at-large. One of the questions asked was whether all parents should be required to vaccinate of people answering "yes" to this question was 66% of the general public and 84% of scientists. Sup 115 members of the general public and 100 scientists. Construct a 98 % confidence interval for the population proportions. Let p, be the proportion of the general public who feels that all parents should be required to vacci proportion of scientists who feels that all parents should be required to vaccinate their children. Round your answers to four decimal places.

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**Survey Overview: Vaccination Requirements**

In July 2011, the Pew Research Center conducted a survey to gauge opinions on science-related questions from two independent random samples: scientists and the general public. One of the key questions asked was whether all parents should be required to vaccinate their children. From the respondents, 66% of the general public and 84% of scientists agreed with the requirement.

**Sample Details:**
- General Public: 115 respondents
- Scientists: 100 respondents

**Statistical Task:**
Construct a 98% confidence interval to estimate the difference in population proportions, \( p_1 - p_2 \).

**Definitions:**
- \( p_1 \): Proportion of the general public in favor of mandatory vaccination for children.
- \( p_2 \): Proportion of scientists in favor of mandatory vaccination for children.

**Instructions:**
Calculate the 98% confidence interval for \( p_1 - p_2 \) and round your answers to four decimal places.

\[ < p_1 - p_2 < \]

This calculation helps understand the potential difference in opinion between these groups based on the sample data.
Transcribed Image Text:**Survey Overview: Vaccination Requirements** In July 2011, the Pew Research Center conducted a survey to gauge opinions on science-related questions from two independent random samples: scientists and the general public. One of the key questions asked was whether all parents should be required to vaccinate their children. From the respondents, 66% of the general public and 84% of scientists agreed with the requirement. **Sample Details:** - General Public: 115 respondents - Scientists: 100 respondents **Statistical Task:** Construct a 98% confidence interval to estimate the difference in population proportions, \( p_1 - p_2 \). **Definitions:** - \( p_1 \): Proportion of the general public in favor of mandatory vaccination for children. - \( p_2 \): Proportion of scientists in favor of mandatory vaccination for children. **Instructions:** Calculate the 98% confidence interval for \( p_1 - p_2 \) and round your answers to four decimal places. \[ < p_1 - p_2 < \] This calculation helps understand the potential difference in opinion between these groups based on the sample data.
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