The Quality of Oil Is Measured in API Gravity Degrees

question 212

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 Minitab 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 $$\begin{array} { | l | r | r | r | r | } \hline \text { Predictor } & \text { Coef } & \text { StDev } & \mathrm { T } & \mathrm { P } \\\hline \text { Constant } & 9.4349 & 0.2867 & 32.91 & 0.000 \\\hline \text { Degrees } & 0.095235 & 0.008220 & 11.59 & 0.000 \\\hline\end{array}$$ S = 0.1314 R-Sq = 92.46% R-Sq(adj) = 91.7%
Analysis of Variance $$\begin{array} { | l | r | r | r | r | r | } \hline \text { Source } & \text { DF } & \text { SS } & \text { MS } & \text { F } & \text { P } \\\hline \text { Regression } & 1 & 2.3162 & 2.3162 & 134.24 & 0.000 \\\hline \text { Residual Error } & 11 & 0.1898 & 0.0173 & & \\\hline \text { Total } & 12 & 2.5060 & & & \\\hline\end{array}$$ Conduct a test of the population coefficient of correlation to determine at the 5% significance level whether a linear relationship exists between the quality of oil and price per barrel.

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Definitions:

Glucose

A simple sugar that is an important energy source in living organisms and is a component of many carbohydrates.

Urethra

A tube that connects the urinary bladder to the urinary meatus for the removal of fluids from the body.

Meatus

A natural passage or opening in the body, such as the external opening of the urethra.

Medulla

The inner region of an organ or tissue, especially the medulla oblongata in the brain or the inner part of the kidney.