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. An article reported the accompanying observations on x = TOST time (hr) and y = RBOT time (min) for 12 oil specimens. TOST 4200 3600 3750 3625 4050 3100 RBOT 370 340 375 305 350 210 TOST 4670 RBOT 450 4500 395 3500 285 2900 3750 3350 260 345 285 (a) Calculate the value of the sample correlation coefficient. (Round your answer to four decimal places.) r = Interpret the value of the sample correlation coefficient. The value of r indicates that there is a strong, positive linear relationship between TOST and RBOT. The value of r indicates that there is a strong, negative linear relationship between TOST and RBOT ○ The value of r indicates that there is a weak, negative linear relationship between TOST and RBOT. O The value of r indicates that there is a weak, positive linear relationship between TOST and RBOT. (b) How would the value of r be affected if we had let x = RBOT time and y = TOST time? O The value of r would increase. O The value of r would decrease. The value of r would be multiplied by -1. O The value of r would remain the same. (c) How would the value of r be affected if RBOT time were expressed in hours? ○ The value of r would decrease. O The value of r would remain the same. O The value of r would be multiplied by -1. O The value of r would increase. (d) Construct a normal probability plot for TOST time. TOST (hr) 5000 4500. 4000 3500 3000 2 -1 0 2 о Construct a normal probability plot for RBOT time. RBOT (min) 450 400 350 300 250 о -2 -1 0 1 2 10 TOST (hr) 5000 TOST (hr) TOST (hr) 5000 5000! 4500 4500 4500 4000 4000 4000 3500 3500 3500 3000- 3000 3000 1 ด RBOT (min) 450. 400 350 300 250 -1 RBOT (min) 450. 400 350 300 250 -2 -1 0 1 2 Comment. O Both TOST and RBOT time appear to come from normal populations. ORBOT time appears normal, while TOST time appears nonnormal. Both TOST and RBOT time appear to come from nonnormal population. ○ TOST time appears normal, while RBOT time appears nonnormal. (e) Carry out a test of hypotheses to decide whether RBOT Time and TOST time are linearly related. (Use α = 0.05.) State the appropriate null and alternative hypotheses. ○ Hop = 0 HP < 0 OHO: P = 0 Hp 0 O Hop 0 Hop=0 OH₁: p=0 H:p>O Calculate the test statistic and determine the P-value. (Round your test statistic to two decimal places and your P-value to three decimal places.) t = P-value = State the conclusion in the problem context. ◇ Fail to reject Ho. The model is useful. O Reject H. The model is not useful. Reject Ho. The model is useful. O Fail to reject H₁. The model is not useful. RBOT (min) 450 400 350 300 250 -1 0