Question

Vehicle Name	Weight
Cadillac CTS VVT 4dr	3694
Cadillac Deville 4dr	3984
Cadillac Deville DTS 4dr	4044
Cadillac Seville SLS 4dr	3992
Lincoln LS V6 Luxury 4dr	3681
Lincoln LS V6 Premium 4dr	3681
Lincoln LS V8 Sport 4dr	3768
Lincoln LS V8 Ultimate 4dr	3768
Lincoln Town Car Signature 4dr	4369
Lincoln Town Car Ultimate 4dr	4369
Lincoln Town Car Ultimate L 4dr	4474

In what follows use any of the following tests/procedures: Regression, multiple regressions, confidence intervals, one-sided t-test or two-sided t-test. All the procedures should be done with 5% P-value or 95% confidence interval

Upload CARS data. SETUP: It is believed that Lincolns are heavier than Cadillac. Given the data your job is to confirm or disprove this belief. (CAREFULL: sort the data in order to extract the needed information).

9. What test/procedure did you perform?

• a. One-sided t-test
• b. Regression
• c. Two-sided t-test
• d. ​​Confidence interval

10. What is the P-value/margin of error?

• a. 339.06234
• b. 0.598587029
• c. 0.299293514
• d. 8.065421
• e. ​​None of these

11. Statistical Interpretation

• a. Due to small margin of error we are confident that the average mpg is above 3500.
• b. Since P-value is large we cannot claim that the averages are different.
• c. Since P-value is very small we are confident that the slope of regression line is not zero.
• d. None of these

12. Conclusion

• a. Yes, I am confident that the above assertion is correct.
• b. No, we cannot claim that the above assertion is correct.

Task 2

Answer 1

(9) One-sided t test

(10)

Data:     

n1 = 7    

n2 = 4    

x1-bar = 4015.71    

x2-bar = 3928.5    

s1 = 366.62    

s2 = 158.58    

Hypotheses:    

Ho: μ1 ≤ μ2    

Ha: μ1 > μ2    

Decision Rule:    

α = 0.05    

Degrees of freedom = 7 + 4 - 2 = 9

Critical t- score = 1.83311292   

Reject Ho if t > 1.83311292   

Test Statistic:    

Pooled SD, s = √[{(n1 - 1) s1^2 + (n2 - 1) s2^2} / (n1 + n2 - 2)] = √(((7 - 1) * 366.62^2 + (4 - 1) * 158.58^2)/(7 + 4 - 2)) = 313.0325144

SE = s * √{(1 /n1) + (1 /n2)} = 313.032514392142 * √((1/7) + (1/4)) = 196.2035118

t = (x1-bar -x2-bar)/SE = (4015.71 - 3928.5)/196.203511849061 = 0.444487457

p- value = 0.3335932    

Decision (in terms of the hypotheses):

Since 0.44448746 < 1.833112923 we fail to reject Ho

Conclusion (in terms of the problem):

There is no sufficient evidence that Lincolns are heavier than Cadillac

p- value answer: None of these

(11) None of these

(12) Yes, I am confident that the above assertion is correct