In April 2022, the Pew Research Center conducted a representative telephone survey to access whether U.S. teens felt overwhelmed by social media, and whether those results differed by gender. The results from the survey are summarized below: Overwhelmed Not Overwhelmed Total Boys 206 438 644 Girls 302 370 672 Total 508 808 1316 a. What is the overall (conservative) margin of error for this survey-give your answer to the nearest tenth of a percent. b. Find a 95% confidence interval for the percent of teens that felt overwhelmed to the nearest tenth of a percent

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In April 2022, the Pew Research Center conducted a representative telephone survey to access whether U.S. teens felt overwhelmed by social media, and whether those results differed by gender. The results from the survey are summarized below:
Conditions check:

Test statistic and P-value:

Decision:

Conclusion in context:
Transcribed Image Text:Conditions check: Test statistic and P-value: Decision: Conclusion in context:
### Survey on Teens' Feelings of Overwhelmed by Social Media

In April 2022, the Pew Research Center conducted a representative telephone survey to determine whether U.S. teens felt overwhelmed by social media, and whether those results differed by gender. The summarized results from the survey are as follows:

| Feeling          | Boys | Girls | Total |
|------------------|------|-------|-------|
| Overwhelmed      | 206  | 302   | 508   |
| Not Overwhelmed  | 438  | 370   | 808   |
| Total            | 644  | 672   | 1316  |

#### a. Overall (Conservative) Margin of Error for the Survey
- **Question**: What is the overall (conservative) margin of error for this survey—give your answer to the nearest tenth of a percent.

#### b. 95% Confidence Interval for the Percent of Teens Feeling Overwhelmed
- **Question**: Find a 95% confidence interval for the percent of teens that felt overwhelmed to the nearest tenth of a percent.

These questions aim to critically assess the statistical reliability and significance of the survey results, contributing to a deeper understanding of the data provided.

### Graphs or Diagrams
The table provides the numerical data for the survey, categorized by gender and whether they feel overwhelmed by social media or not. 
- **Rows**: Represent the feelings of being overwhelmed or not overwhelmed.
- **Columns**: Separate the data by gender (Boys, Girls) and provide combined totals.
  
This structured format helps in clearly visualizing the distribution of responses and comparing the data across different groups.
Transcribed Image Text:### Survey on Teens' Feelings of Overwhelmed by Social Media In April 2022, the Pew Research Center conducted a representative telephone survey to determine whether U.S. teens felt overwhelmed by social media, and whether those results differed by gender. The summarized results from the survey are as follows: | Feeling | Boys | Girls | Total | |------------------|------|-------|-------| | Overwhelmed | 206 | 302 | 508 | | Not Overwhelmed | 438 | 370 | 808 | | Total | 644 | 672 | 1316 | #### a. Overall (Conservative) Margin of Error for the Survey - **Question**: What is the overall (conservative) margin of error for this survey—give your answer to the nearest tenth of a percent. #### b. 95% Confidence Interval for the Percent of Teens Feeling Overwhelmed - **Question**: Find a 95% confidence interval for the percent of teens that felt overwhelmed to the nearest tenth of a percent. These questions aim to critically assess the statistical reliability and significance of the survey results, contributing to a deeper understanding of the data provided. ### Graphs or Diagrams The table provides the numerical data for the survey, categorized by gender and whether they feel overwhelmed by social media or not. - **Rows**: Represent the feelings of being overwhelmed or not overwhelmed. - **Columns**: Separate the data by gender (Boys, Girls) and provide combined totals. This structured format helps in clearly visualizing the distribution of responses and comparing the data across different groups.
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