MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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# Do Teen Problems Differ Based on Income Level?

**Objective:**
Analyze whether US teens consider anxiety/depression a major problem based on household income.

**Data Source:**
Table 3.10 reports responses from teens on whether they perceive anxiety/depression as a significant issue, segmented by household income.

**Questions:**

a. **Proportion Analysis:**  
   - Calculate the proportion of teens from households earning less than $75,000 who view it as a major problem.
   - Calculate the proportion of teens from households earning more than $75,000 with the same viewpoint.

b. **Notation and Sample Statistic:**  
   - Define symbols and values for sample statistics.

c. **Standard Error Calculation:**  
   - Use software like StatKey to find the standard error using a bootstrap distribution.

d. **Confidence Interval:**  
   - Determine a 95% confidence interval for the difference in proportions.

e. **Analysis and Conclusion:**  
   - Evaluate if there's a significant difference in perception based on income, using the confidence interval.

**Table 3.10: Anxiety and Depression as Major Problems Among Teens**

| Income                | Major Problem | Not Major Problem | Total |
|-----------------------|---------------|-------------------|-------|
| Less than $75,000     | 386           | 150               | 536   |
| More than $75,000     | 258           | 126               | 384   |
| Total                 | 644           | 276               | 920   |

This table categorizes teens’ responses based on household income, highlighting the number who consider anxiety/depression a major problem versus those who do not.
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Transcribed Image Text:# Do Teen Problems Differ Based on Income Level? **Objective:** Analyze whether US teens consider anxiety/depression a major problem based on household income. **Data Source:** Table 3.10 reports responses from teens on whether they perceive anxiety/depression as a significant issue, segmented by household income. **Questions:** a. **Proportion Analysis:** - Calculate the proportion of teens from households earning less than $75,000 who view it as a major problem. - Calculate the proportion of teens from households earning more than $75,000 with the same viewpoint. b. **Notation and Sample Statistic:** - Define symbols and values for sample statistics. c. **Standard Error Calculation:** - Use software like StatKey to find the standard error using a bootstrap distribution. d. **Confidence Interval:** - Determine a 95% confidence interval for the difference in proportions. e. **Analysis and Conclusion:** - Evaluate if there's a significant difference in perception based on income, using the confidence interval. **Table 3.10: Anxiety and Depression as Major Problems Among Teens** | Income | Major Problem | Not Major Problem | Total | |-----------------------|---------------|-------------------|-------| | Less than $75,000 | 386 | 150 | 536 | | More than $75,000 | 258 | 126 | 384 | | Total | 644 | 276 | 920 | This table categorizes teens’ responses based on household income, highlighting the number who consider anxiety/depression a major problem versus those who do not.
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