The Quality of Oil Is Measured in API Gravity Degrees

question 117

Essay

The quality of oil is measured in API gravity degrees - the higher the degrees API, the higher the quality. The table shown below is produced by an expert in the field, who believes that there is a relationship between quality and price per barrel. $$\begin{array} { | c | c | } \hline \text { Oil degrees API } & \text { Price per barrel (in } \$ \text { ) } \\\hline 27.0 & 12.02 \\\hline 28.5 & 12.04 \\\hline 30.8 & 12.32 \\\hline 31.3 & 12.27 \\\hline 31.9 & 12.49 \\\hline 34.5 & 12.70 \\\hline 34.0 & 12.80 \\\hline 34.7 & 13.00 \\\hline 37.0 & 13.00 \\\hline 41.0 & 13.17 \\\hline 41.0 & 13.19 \\\hline 38.8 & 13.22 \\\hline 39.3 & 13.27 \\\hline\end{array}$$ A partial computer output follows.
Descriptive Statistics $$\begin{array} { | l | r | r | r | r | } \hline \text { Variable } & \mathrm { N } & \text { Mean } & \text { StDev } & \text { SE Mean } \\\hline \text { Degrees } & 13 & 34.60 & 4.613 & 1.280 \\\hline \text { Frice } & 13 & 12.730 & 0.457 & 0.127 \\\hline\end{array}$$ Covariances $$\begin{array} { | l | r | r | } \hline & \text { Degrees } & \text { Price } \\\hline \text { Degrees } & 21.281667 & \\\hline \text { Price } & 2.026750 & 0.208833 \\\hline\end{array}$$ Regression Analysis $$\begin{array} { | l | r | r | r | r | } \hline \text { Fredictor } & \text { Coef } & \text { StDev } & \mathrm { T } & \mathrm { P } \\\hline \text { Constant } & 9.4349 & 0.2867 & 32.91 & 0.000 \\\hline \text { Degrees } & 0.095235 & 0.008220 & 11.59 & 0.000 \\\hline\end{array}$$ S = 0.1314 R-Sq = 92.46% R-Sq(adj) = 91.7%
Analysis of Variance $$\begin{array} { | l | r | r | r | r | r | } \hline \text { Source } & \text { DF } & \text { SS } & \text { MS } & \mathrm { F } & \mathrm { P } \\\hline \text { Regression } & 1 & 2.3162 & 2.3162 & 134.24 & 0.000 \\\hline \text { Residual Error } & 11 & 0.1898 & 0.0173 & & \\\hline \text { Total } & 12 & 2.5060 & & & \\\hline\end{array}$$ Conduct a test of the population slope to determine at the 5% significance level whether a linear relationship exists between the quality of oil and price per barrel.

---

Definitions:

Pacemaker

A medical device implanted in the chest to help control abnormal heart rhythms, using electrical impulses to prompt the heart to beat at a normal rate.

Wireless LAN

A local area network that enables devices to communicate without physical cables, using radio waves for connectivity.

Connected Vehicle

Refers to cars, buses, trucks, and other mobile machines that use internet connectivity and other technologies to communicate with each other and with infrastructure, enhancing safety and efficiency.

Self-Driving Technology

Revolutionary technology in vehicles that allows them to navigate and operate without human intervention.