At a Recent Music Concert, a Survey Was Conducted That

question 199

Essay

At a recent music concert, a survey was conducted that asked a random sample of 20 people their age and how many concerts they have attended since the beginning of the year. The following data were collected. $$\begin{array} { | l | c | c | c | c | c | c | c | c | c | c | } \hline \text { Age } & 62 & 57 & 40 & 49 & 67 & 54 & 43 & 65 & 54 & 41 \\\hline \text { Number of concerts } & 6 & 5 & 4 & 3 & 5 & 5 & 2 & 6 & 3 & 1 \\\hline\end{array}$$ $$\begin{array} { | l | c | c | c | c | c | c | c | c | c | c | } \hline \text { Age } & 44 & 48 & 55 & 60 & 59 & 63 & 69 & 40 & 38 & 52 \\\hline \text { Number of Concerts } & 3 & 2 & 4 & 5 & 4 & 5 & 4 & 2 & 1 & 3 \\\hline\end{array}$$ $\begin{array}{ll}\text { SUMMARY OUTPUT }&\text { DESCRIPTIVE STATISTICS }\\\begin{array}{lc}\hline {\text { Reqression Statiatics }} \\\hline \text { Multiple R } & 0.80203 \\\text { R Square } & 0.64326 \\\text { Adjusted R Square } & 0.62344 \\\text { Standard Error } & 0.93965 \\\text { Observations } & 20 \\\hline\end{array}&\begin{array}{lclc}\hline {\text { Age }} &&{\text { Concerts }} \\\hline \text { Mean } & 53 & \text { Mean } & 3.65 \\\text { Standard Error } & 2.1849 & \text { Standard Error } & 0.3424 \\\text { Standard Deviation } & 9.7711 & \text { Standard Deviation } & 1.5313 \\\text { Sample Variance } & 95.4737 & \text { Sample Variance } & 2.3447 \\\text { Count } & 20 & \text { Count } & 20\\\hline\end{array}\\\end{array}$
$\text { SPEARMAN RANK CORRELATION COEFFICIENT }=0.8306$

$\begin{array}{lccccc} \text { ANOVA }\\\hline& \text { df } & \text { SS } & \text { MS } & F & \text { Significance F } \\\hline \text { Regression } & 1 & 28.65711 & 28.65711 & 32.45653 & 2.1082 \mathrm{E}-05 \\\text { Residual } & 18 & 15.89289 & 0.88294 & & \\\text { Total } & 19 & 44.55 & & &\\\hline\end{array}$

$\begin{array}{lcccccc}\hline & \text { Coefficients } & \text {Standard Error } & \text { t Stat } & \text { P-value } & \text { Lower } 95 \% & \text { Upper 95\% } \\\hline \text { Intercept } & -3.01152 & 1.18802 & -2.53491 & 0.02074 & -5.50746 & -0.5156 \\\text { Age } & 0.12569 & 0.02206 & 5.69706 & 0.00002 & 0.07934 & 0.1720\end{array}$ Conduct a test of the population slope to determine at the 5% significance level whether a linear relationship exists between age and number of concerts attended.

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Definitions:

George Fitzhugh

A nineteenth-century American social theorist known for his defense of slavery as a positive good, arguing that slavery ensured the welfare and civilization of society as a whole.

Yeoman Farmers

Small landowners (the majority of white families in the Old South) who farmed their own land and usually did not own slaves.

Urban Slaves

Refers to enslaved people who lived and worked in urban settings, often in roles different from their counterparts on plantations, such as artisans or domestic workers.

Civil War

Refers to the American Civil War, fought from 1861 to 1865, primarily over the issues of slavery and states' rights, resulting in the preservation of the Union.