To determine the relationship between pressure and volume, we can calculate the correlation coefficient between these two variables.
Here are the pressure and volume datasets provided:
[tex]\[
\begin{array}{|c|c|}
\hline
\text{Pressure (torr)} & \text{Volume (mL)} \\
\hline
750 & 30 \\
\hline
950 & 22 \\
\hline
1150 & 19 \\
\hline
1350 & 15 \\
\hline
1500 & 13 \\
\hline
1650 & 10 \\
\hline
\end{array}
\][/tex]
The correlation coefficient measures the strength and direction of the linear relationship between two variables. It ranges from -1 to 1. A correlation coefficient close to 1 indicates a strong positive linear relationship, a coefficient close to -1 indicates a strong negative linear relationship, and a coefficient close to 0 indicates no linear relationship.
For the given pressure and volume data, the correlation coefficient is approximately [tex]\(-0.982\)[/tex]. This value is very close to -1, indicating a strong negative linear relationship between pressure and volume.
A negative correlation implies that as one variable increases, the other variable tends to decrease. With our computed correlation coefficient of [tex]\(-0.982\)[/tex], we can conclude that as the pressure increases, the volume tends to decrease.
Thus, the accurate statement that represents the relationship between pressure and volume is:
As pressure increases, volume decreases.
