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3-94 Do Teen Problems Differ Based on Income Level? Exercise 3.93 introduces a survey that asked US teens whether they consider anxiety/depression a major problem among their peers. Table 3.10 shows the results of whether teens said it was a major problem or not, based on household income level of the teens. We are interested in estimating the difference in proportion who think it is a major problem, between the two groups. a. What proportion of teens in households with income below $75,000 think it is a major problem? What proportion of teens in households making more than $75,000 think it is a major problem? b. Give notation and the value of the relevant sample statistic. c. Use StatKey or other technology to find the standard error for this statistic using a bootstrap distribution. d. Use the standard error to find a 95% confidence interval for the difference in proportions. e. Can we conclude that there is a difference in the proportion believing anxiety/depression is a major problem for their peers, between those with household income below $75,000 and those with income above that level? Justify your answer using the confidence interval. TABLE 3.10 Are anxiety and depression major problems for teens? Income Major problem Not major problem Total 536 384 920 Less than $75,000 More than $75,000 Total 386 258 644 150 126 276

3-94 Do Teen Problems Differ Based on Income Level? Exercise 3.93 introduces a survey that asked US teens whether they consider anxiety/depression a major problem among their peers. Table 3.10 shows the results of whether teens said it was a major problem or not, based on household income level of the teens. We are interested in estimating the difference in proportion who think it is a major problem, between the two groups. a. What proportion of teens in households with income below $75,000 think it is a major problem? What proportion of teens in households making more than $75,000 think it is a major problem? b. Give notation and the value of the relevant sample statistic. c. Use StatKey or other technology to find the standard error for this statistic using a bootstrap distribution. d. Use the standard error to find a 95% confidence interval for the difference in proportions. e. Can we conclude that there is a difference in the proportion believing anxiety/depression is a major problem for their peers, between those with household income below $75,000 and those with income above that level? Justify your answer using the confidence interval. TABLE 3.10 Are anxiety and depression major problems for teens? Income Major problem Not major problem Total 536 384 920 Less than $75,000 More than $75,000 Total 386 258 644 150 126 276

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
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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.
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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