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Teams with varying numbers of players are playing a group card game. The time taken by each team to complete one game is given in the table. What is the relationship between the two variables?

[tex]\[
\begin{tabular}{|c|c|}
\hline
Number of Players on the Team & Time Taken to Complete Game (in minutes) \\
\hline
1 & 32 \\
\hline
2 & 26 \\
\hline
3 & 20 \\
\hline
4 & 14 \\
\hline
5 & 8 \\
\hline
\end{tabular}
\][/tex]

A. Positive linear association
B. Exponential relationship
C. Negative linear association
D. No relationship



Answer :

GinnyAnswer
To determine the relationship between the number of players and the time taken to complete the game, we need to analyze the data provided:

[tex]\[ \begin{array}{|c|c|} \hline \text{Number of Players on the Team} & \text{Time Taken to Complete Game (in minutes)} \\ \hline 1 & 32 \\ \hline 2 & 26 \\ \hline 3 & 20 \\ \hline 4 & 14 \\ \hline 5 & 8 \\ \hline \end{array} \][/tex]

The correlation coefficient is a measure of the strength and direction of the linear relationship between two variables. After calculating this correlation coefficient, we find that it is [tex]\(-1.0\)[/tex].

A correlation coefficient of [tex]\(-1.0\)[/tex] indicates a perfect negative linear relationship between the number of players and the time taken to complete the game. This means that as the number of players increases, the time taken to complete the game consistently decreases in a linear manner.

Given the provided data and the calculated correlation coefficient [tex]\(-1.0\)[/tex], we can conclude that the relationship between the number of players and the time taken to complete the game is best described by:

C. negative linear association

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