6.5.1: Practice Problems Corequisite S.5
- Page ID
- 148637
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)The table below displays social and health data on a random sample of 11 counties in the United States. For each county, the table shows the percentage of adults who have a graduate degree, the percentage of adults who smoke cigarettes, and the percentage of children living with one parent. The data was collected from surveys in 2010 and analyzed in the 2016 report.18
| County | Percentage of Adults with a Graduate Degree | Percentage of Adults who Smoke Cigarettes | Percentage of Children Living with One Parent |
| Newport News City, Virginia | 8 | 23 | 43 |
| Washington County, Florida | 5 | 27 | 35 |
| Warrick County, Indiana | 9 | 14 | 22 |
| San Mateo County, California | 17 | 11 | 23 |
| Cullman County, Alabama | 5 | 22 | 27 |
| Allegheny County, Pennsylvania | 14 | 19 | 33 |
| Bourbon County, Kansas | 7 | 19 | 31 |
| Bedford County, Virginia | 9 | 19 | 23 |
| Randolph County, Alabama | 5 | 28 | 44 |
| St. Bernard Parish, Louisiana | 3 | 22 | 43 |
| Hardin County, Ohio | 6 | 31 | 29 |
- Which variable in the data set above has the lowest variability? Use the ranges or estimate the standard deviations of each variable.
(2) Which variable in the data set above has the highest variability? Use the ranges or estimate the standard deviations of each variable.
For Questions 3-8, compute the mean and standard deviation for each variable and complete the table. Round each answer to one decimal place.
| Percent of Adults with a Graduate Degree | Percent of Adults who Smoke Cigarettes | Percent of Children Living with One Parent | |
| Mean | (3) | (4) | (5) |
| SD | (6) | (7) | (8) |
(9) The scatterplot shows the percentage of adults in a county who have a graduate degree and the percentage of adults in a county who smoke cigarettes. What can you conclude about the relationship between these two variables based on the sample data?
(10) Develop a linear model to summarize the data. Use the points (0,29) and (17,12). Let S be the percentage of adults in a county who smoke and G be the percentage of adults in a county who have a graduate degree.
(11) Use the linear model to predict the percentage of adults who smoke cigarettes in a county if 12% of adults in the county have a graduate degree.
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