The Turbine Oil Oxidation Test (TOST) and the Rotating Bomb Oxidation Test (RBOT) are two different procedures for evaluating the oxidation stability of steam turbine oils. The accompanying observations on x = TOST time (hr) and y = RBOT time (min) for 12 oil specimens have been reported: $$\begin{array} { l c c c c c c }
\hline \text { TOST } & 4200 & 3600 & 3750 & 3675 & 4050 & 2770 \
\hline \text { RBOT } & 370 & 340 & 375 & 310 & 350 & 200 \
\hline & & & & & & \
\hline \text { TOST } & 4870 & 4500 & 3450 & 2700 & 3750 & 3300 \
\hline \text { RBOT } & 400 & 375 & 285 & 225 & 345 & 285 \
\hline
\end{array}$$
a. Calculate and interpret the value of the sample correlation coefficient .
b. How would the value of r be affected if we had let x = RBOT time and y = TOST time?
c. How would the value of r be affected if RBOT time were expressed in hours?
d. Normal probability plots indicate that Both TOST and ROBT time appear to have come from normally distributed populations. Carry out a test of hypotheses to decide whether RBOT time and TOST time are linearly related.

Question

The Turbine Oil Oxidation Test (TOST) and the Rotating Bomb Oxidation Test (RBOT) are two different procedures for evaluating the oxidation stability of steam turbine oils. The accompanying observations on x = TOST time (hr) and y = RBOT time (min) for 12 oil specimens have been reported: $$\begin{array} { l c c c c c c } 
\hline \text { TOST } & 4200 & 3600 & 3750 & 3675 & 4050 & 2770 \
\hline \text { RBOT } & 370 & 340 & 375 & 310 & 350 & 200 \
\hline & & & & & & \
\hline \text { TOST } & 4870 & 4500 & 3450 & 2700 & 3750 & 3300 \
\hline \text { RBOT } & 400 & 375 & 285 & 225 & 345 & 285 \
\hline
\end{array}$$ 
a. Calculate and interpret the value of the sample correlation coefficient .
b. How would the value of r be affected if we had let x = RBOT time and y = TOST time?
c. How would the value of r be affected if RBOT time were expressed in hours?
d. Normal probability plots indicate that Both TOST and ROBT time appear to have come from normally distributed populations. Carry out a test of hypotheses to decide whether RBOT time and TOST time are linearly related.

Quizplus · Accepted Answer

The Answer of The Turbine Oil Oxidation Test (TOST) and the Rotating Bomb Oxidation Test (RBOT) are two different procedures for evaluating the oxidation stability of steam turbine oils. The accompanying observations on x = TOST time (hr) and y = RBOT time (min) for 12 oil specimens have been reported: $$\begin{array} { l c c c c c c } 
\hline \text { TOST } & 4200 & 3600 & 3750 & 3675 & 4050 & 2770 \
\hline \text { RBOT } & 370 & 340 & 375 & 310 & 350 & 200 \
\hline & & & & & & \
\hline \text { TOST } & 4870 & 4500 & 3450 & 2700 & 3750 & 3300 \
\hline \text { RBOT } & 400 & 375 & 285 & 225 & 345 & 285 \
\hline
\end{array}$$ 
a. Calculate and interpret the value of the sample correlation coefficient .
b. How would the value of r be affected if we had let x = RBOT time and y = TOST time?
c. How would the value of r be affected if RBOT time were expressed in hours?
d. Normal probability plots indicate that Both TOST and ROBT time appear to have come from normally distributed populations. Carry out a test of hypotheses to decide whether RBOT time and TOST time are linearly related.