Question

core: 0 of 1 pt 2 of 3 (1 complete) HW Score: 22.33%, 0.67 of 3 pts 0.3.9 Question Help The Minitab output shown below was obtained by using paired data consisting of weights (in lb) of 29 cars and their highway fuel consumption amounts (in migal). Along with the paired sample data, Mintab was also given a car weight of 3000 lb to be used for predicting the highway fuel consumption amount. Use the information provided in the display to determine the value of the linear correlation coefficient. (Be careful to correctly identify the sign of the correlation coefficient. Given that there are 29 pairs of data, is there sufficient evidence to support a claim of linear correlation between the weights of cars and their highway fuel consumption amounts? Cick the icon to view the Minitab display. The linear correlation coefficient is -0.802 Minitab output (Round to three decimal places as needed) Is there sufficient evidence to support a claim of linear correlation? The regression equation is Highway = 50.5-000501 Weight Yos No P Predictor Coef Constant 50.465 Weight -0.0050096 SE Coef 2883 0.0007962 T 17.15 -7.79 0.000 0.000 s - 2.27663 R-Sq - 644% R-Saadj) - 61.7% Predicted Values for New Observations New Obs 1 Fit 35.436 SE FI 0.499 95% CI (34.435, 36 437) 95% PI (30.846, 40.027) Values of Predictors for New Observations New Obs Weight 1 3000 Click to select your answer and then click Check Answer Final Chock All parts showing Show All X 115795745 525 116289228 67.ips 116908578.213...po media 05.95.png 116908578_213.jpg 80 DI DOO F4 34 F7 EM F9 # ( + $ 4 % 5 & 7 2 3 6 8 9 0 delete { Q W E R T Y U 0 Р Ti А S D G H J к L

Answer 1

sample size (n) = 29

a).the linear correlation coefficient is :-

$r=\sqrt{R^2}=\sqrt{0.644}\approx \mathbf{-0.802}$ [ R squared = 64.4%= 0.644 ]

[ the value of r is negative, because, the sign of coefficient of weight is negative..]

b). hypothesis:-

$H_{0}:\rho=0$

$H_{1}:\rho\neq0$

df = (n-2) = (29-2) = 27

r critical value for alpha=0.05, df = 27, both tailed test be:-

$r_{critical}=\pm 0.367$

decision:-

$\left | r \right |=0.802>\left |r_{critical} \right |= 0.367$

we reject the null hypothesis.

YES, there is sufficient evidence to support a claim of linear correlation.

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