At a Recent Music Concert, a Survey Was Conducted That

question 82

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. $$\begin{array} { | l | c | c | c | c | c | c | c | c | c | c | } \hline \text { Age } & 62 & 57 & 40 & 49 & 67 & 54 & 43 & 65 & 54 & 41 \\\hline \text { Number of concerts } & 6 & 5 & 4 & 3 & 5 & 5 & 2 & 6 & 3 & 1 \\\hline\end{array}$$ $$\begin{array} { | l | c | c | c | c | c | c | c | c | c | c | } \hline \text { Age } & 44 & 48 & 55 & 60 & 59 & 63 & 69 & 40 & 38 & 52 \\\hline \text { Number of Concerts } & 3 & 2 & 4 & 5 & 4 & 5 & 4 & 2 & 1 & 3 \\\hline\end{array}$$ $\begin{array}{ll}\text { SUMMARY OUTPUT }&\text { DESCRIPTIVE STATISTICS }\\\begin{array}{lc}\hline {\text { Reqression Statiatics }} \\\hline \text { Multiple R } & 0.80203 \\\text { R Square } & 0.64326 \\\text { Adjusted R Square } & 0.62344 \\\text { Standard Error } & 0.93965 \\\text { Observations } & 20 \\\hline\end{array}&\begin{array}{lclc}\hline {\text { Age }} &&{\text { Concerts }} \\\hline \text { Mean } & 53 & \text { Mean } & 3.65 \\\text { Standard Error } & 2.1849 & \text { Standard Error } & 0.3424 \\\text { Standard Deviation } & 9.7711 & \text { Standard Deviation } & 1.5313 \\\text { Sample Variance } & 95.4737 & \text { Sample Variance } & 2.3447 \\\text { Count } & 20 & \text { Count } & 20\\\hline\end{array}\\\end{array}$
$\text { SPEARMAN RANK CORRELATION COEFFICIENT }=0.8306$

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

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

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