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The Quality of Oil Is Measured in API Gravity Degrees

question 37

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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.  Oil degrees API  Price per barrel (in $ ) 27.012.0228.512.0430.812.3231.312.2731.912.4934.512.7034.012.8034.713.0037.013.0041.013.1741.013.1938.813.2239.313.27\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  Variable N Mean  StDev  SE Mean  Degrees 1334.604.6131.280 Frice 1312.7300.4570.127\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  Degrees  Price  Degrees 21.281667 Price 2.0267500.208833\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  Fredictor  Coef  StDev TP Constant 9.43490.286732.910.000 Degrees 0.0952350.00822011.590.000\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  Source  DF  SS  MS FP Regression 12.31622.3162134.240.000 Residual Error 110.18980.0173 Total 122.5060\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 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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