In: Statistics and Probability
Vehicle Name | Weight |
Jaguar X-Type 2.5 4dr | 3428 |
Cadillac CTS VVT 4dr | 3694 |
Jaguar X-Type 3.0 4dr | 3516 |
Cadillac Deville 4dr | 3984 |
Cadillac Deville DTS 4dr | 4044 |
Cadillac Seville SLS 4dr | 3992 |
Jaguar S-Type 3.0 4dr | 3777 |
Jaguar S-Type 4.2 4dr | 3874 |
Jaguar S-Type R 4dr | 4046 |
Jaguar Vanden Plas 4dr | 3803 |
Jaguar XJ8 4dr | 3803 |
Jaguar XJR 4dr | 3948 |
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 and Cadillac have different weigths. 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?
10. What is the P-value/margin of error?
11. Statistical Interpretation
12. Conclusion
Task 2
Data:
Sample 1 | Weight | Sample 2 | Weight | |
Cadillac CTS VVT 4dr | 3694 | Jaguar S-Type 3.0 4dr | 3777 | |
Cadillac Deville 4dr | 3984 | Jaguar S-Type 4.2 4dr | 3874 | |
Cadillac Deville DTS 4dr | 4044 | Jaguar S-Type R 4dr | 4046 | |
Cadillac Seville SLS 4dr | 3992 | Jaguar Vanden Plas 4dr | 3803 | |
Jaguar XJ8 4dr | 3803 | |||
Jaguar XJR 4dr | 3948 | |||
Jaguar X-Type 2.5 4dr | 3428 | |||
Jaguar X-Type 3.0 4dr | 3516 |
A.
Two-sided t-test
i.e Option B is correct.
B.
Difference Scores Calculations
Treatment 1
N1: 4
df1 = N - 1 = 4 - 1 = 3
M1: 3928.5
SS1: 75443
s21 =
SS1/(N - 1) = 75443/(4-1) =
25147.67
Treatment 2
N2: 8
df2 = N - 1 = 8 - 1 = 7
M2: 3774.38
SS2: 302229.88
s22 =
SS2/(N - 1) = 302229.88/(8-1) =
43175.7
T-value Calculation
s2p =
((df1/(df1 +
df2)) * s21) +
((df2/(df2 +
df2)) * s22) =
((3/10) * 25147.67) + ((7/10) * 43175.7) = 37767.29
s2M1 =
s2p/N1
= 37767.29/4 = 9441.82
s2M2 =
s2p/N2
= 37767.29/8 = 4720.91
t = (M1 -
M2)/√(s2M1
+ s2M2) =
154.12/√14162.73 = 1.3
df = 10
p-value = 0.22439 > 0.05 (The result is not significant )
i.e Option C is correct (Closest answer)
C.
Since P-value is large we cannot claim that the averages are different.
i.e Option B is correct.
D.
No, we cannot claim that the above assertion is correct.
i.e Option B is correct.
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