At a Recent Music Concert, a Survey Was Conducted That

question 15

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. $$\begin{array}{l}\begin{array} { | l | c | c | c | c | c | c | c | c | c | c | } \hline \text { Age } & 62 & 57 & 40 & 49 & 67 & 54 & 43 & 65 & 54 & 41 \\\hline \text { Number of concerts } & 6 & 5 & 4 & 3 & 5 & 5 & 2 & 6 & 3 & 1 \\\hline\end{array}\\\\\begin{array} { | l | c | c | c | c | c | c | c | c | c | c | } \hline \text { Age } & 44 & 48 & 55 & 60 & 59 & 63 & 69 & 40 & 38 & 52 \\\hline \text { Number of Concerts } & 3 & 2 & 4 & 5 & 4 & 5 & 4 & 2 & 1 & 3 \\\hline\end{array}\end{array}$$ 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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Definitions:

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A psychological state where individuals experience a deep sense of oneness with a group, often leading to a blurring of personal and group identity.

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The portion of an individual's self-concept derived from perceived membership in a relevant social group.

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The shared belief in the ability of a group to achieve common objectives and influence outcomes in their community.