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. An article reported the accompanying observations on x = TOST time (hr) and y = RBOT time (min) for 12 oil specimens.

TOST	4200	3600	3750	3700	4050	2795
RBOT	370	335	375	305	350	195

TOST	4870	4525	3450	2675	3750	3300
RBOT	400	375	285	225	345	290

(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 weak, positive linear relationship between TOST and RBOT.The value of r indicates that there is a weak, negative linear relationship between TOST and RBOT.    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.

(b) How would the value of r be affected if we had let x = RBOT time and y = TOST time?

The value of r would remain the same.The value of r would be multiplied by −1.    The value of r would decrease.The value of r would increase.

(c) How would the value of r be affected if RBOT time were expressed in hours?

The value of r would decrease.The value of r would increase.    The value of r would be multiplied by −1.The value of r would remain the same.

(d) Construct a normal probability plot for TOST time.

Construct a normal probability plot for RBOT time.

Comment.

TOST time appears normal, while RBOT time appears nonnormal.Both TOST and RBOT time appear to come from normal populations.    RBOT time appears normal, while TOST time appears nonnormal.Both TOST and RBOT time appear to come from nonnormal population.

(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.

H₀: ρ ≠ 0
H_a: ρ = 0H₀: ρ = 0
H_a: ρ ≠ 0    H₀: ρ = 0
H_a: ρ < 0H₀: ρ = 0
H_a: ρ > 0

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 H₀. The model is not useful.Reject H₀. The model is useful.    Reject H₀. The model is not useful.Fail to reject H₀. The model is useful.

Answer 1

(a) Calculate the value of the sample correlation coefficient. (Round your answer to four decimal places.)

r =0.9178

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.

(b) How would the value of r be affected if we had let x = RBOT time and y = TOST time?

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 remain the same.

(d) Construct a normal probability plot for TOST time.

Construct a normal probability plot for RBOT time.

Comment.

Both TOST and RBOT time appear to come from normal populations.   

(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.

H₀: ρ = 0
H_a: ρ ≠ 0    

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	=	7.31
P-value	=	0.000

State the conclusion in the problem context.

Reject H₀. The model is useful.