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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

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.6: Summarizing Categorical Data
Problem 42PFA
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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
Transcribed Image Text: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
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