To determine the strength of the correlation between the hours spent exercising and the hours spent playing video games across five different weeks, we need to analyze the data provided. The data is structured as follows:
[tex]\[
\begin{array}{|c|c|}
\hline
\text{Hours Spent Exercising} & \text{Hours Spent Playing Video Games} \\
\hline
2 & 16 \\
4 & 7 \\
3 & 5 \\
4 & 15 \\
5 & 8 \\
\hline
\end{array}
\][/tex]
To find the strength of the correlation, we follow these steps:
1. Organize the Data: We have the following pairs of data points:
- (2, 16)
- (4, 7)
- (3, 5)
- (4, 15)
- (5, 8)
2. Calculate the Pearson Correlation Coefficient: The Pearson correlation coefficient (r) measures the strength and direction of the linear relationship between two variables. The value of r ranges from -1 to 1, where:
- 1 = perfect positive correlation
- -1 = perfect negative correlation
- 0 = no correlation
Given the computed Pearson correlation coefficient for the provided data is approximately -0.3794.
3. Interpret the Correlation Coefficient:
- If [tex]\( |r| < 0.3 \)[/tex], the correlation is weak.
- If [tex]\( 0.3 \leq |r| < 0.7 \)[/tex], the correlation is moderate.
- If [tex]\( |r| \geq 0.7 \)[/tex], the correlation is strong.
The correlation coefficient [tex]\(-0.3794\)[/tex] falls in the range [tex]\(-0.7 < r < -0.3\)[/tex], indicating a moderate negative correlation.
4. Conclusion: Based on the correlation coefficient calculated, the data indicates that there is a moderate negative correlation between the hours spent exercising and the hours spent playing video games. Thus, the strength of the correlation is "moderate negative correlation".
Therefore, the relationship between the hours spent exercising and the hours spent playing video games is best described as a moderate negative correlation.
