CARS: A sample of 20 cars, including measurements of fuel consumption (city mi/g
ID: 3228076 • Letter: C
Question
CARS: A sample of 20 cars, including measurements of fuel consumption (city mi/gal and highway mi/gal), weight (pounds), number of cylinders, engine displacement (in liters), amount of greenhouse gases emitted (in tons/year), and amount of tailpipe emissions of NOx (in lb/yr).
CAR
CITY
HWY
WEIGHT
CYLINDERS
DISPLACEMENT
MAN/AUTO
GHG
NOX
Chev. Camaro
19
30
3545
6
3.8
M
12
34.4
Chev. Cavalier
23
31
2795
4
2.2
A
10
25.1
Dodge Neon
23
32
2600
4
2
A
10
25.1
Ford Taurus
19
27
3515
6
3
A
12
25.1
Honda Accord
23
30
3245
4
2.3
A
11
25.1
Lincoln Cont.
17
24
3930
8
4.6
A
14
25.1
Mercury Mystique
20
29
3115
6
2.5
A
12
34.4
Mitsubishi Eclipse
22
33
3235
4
2
M
10
25.1
Olds. Aurora
17
26
3995
8
4
A
13
34.4
Pontiac Grand Am
22
30
3115
4
2.4
A
11
25.1
Toyota Camry
23
32
3240
4
2.2
M
10
25.1
Cadillac DeVille
17
26
4020
8
4.6
A
13
34.4
Chev. Corvette
18
28
3220
8
5.7
M
12
34.4
Chrysler Sebring
19
27
3175
6
2.5
A
12
25.1
Ford Mustang
20
29
3450
6
3.8
M
12
34.4
BMW 3-Series
19
27
3225
6
2.8
A
12
34.4
Ford Crown Victoria
17
24
3985
8
4.6
A
14
25.1
Honda Civic
32
37
2440
4
1.6
M
8
25.1
Mazda Protege
29
34
2500
4
1.6
A
9
25.1
Hyundai Accent
28
37
2290
4
1.5
A
9
34.4
Is there evidence that automatic cars are more common than manual cars?
Use a 0.05 significance level to conduct a suitable hypotheses test using the dataset MAN/AUTO as a sample to conduct your test. Set hypotheses, find your point estimate, determine the sampling distribution, find the test statistic, find the p-value and
conclude the test.
CAR
CITY
HWY
WEIGHT
CYLINDERS
DISPLACEMENT
MAN/AUTO
GHG
NOX
Chev. Camaro
19
30
3545
6
3.8
M
12
34.4
Chev. Cavalier
23
31
2795
4
2.2
A
10
25.1
Dodge Neon
23
32
2600
4
2
A
10
25.1
Ford Taurus
19
27
3515
6
3
A
12
25.1
Honda Accord
23
30
3245
4
2.3
A
11
25.1
Lincoln Cont.
17
24
3930
8
4.6
A
14
25.1
Mercury Mystique
20
29
3115
6
2.5
A
12
34.4
Mitsubishi Eclipse
22
33
3235
4
2
M
10
25.1
Olds. Aurora
17
26
3995
8
4
A
13
34.4
Pontiac Grand Am
22
30
3115
4
2.4
A
11
25.1
Toyota Camry
23
32
3240
4
2.2
M
10
25.1
Cadillac DeVille
17
26
4020
8
4.6
A
13
34.4
Chev. Corvette
18
28
3220
8
5.7
M
12
34.4
Chrysler Sebring
19
27
3175
6
2.5
A
12
25.1
Ford Mustang
20
29
3450
6
3.8
M
12
34.4
BMW 3-Series
19
27
3225
6
2.8
A
12
34.4
Ford Crown Victoria
17
24
3985
8
4.6
A
14
25.1
Honda Civic
32
37
2440
4
1.6
M
8
25.1
Mazda Protege
29
34
2500
4
1.6
A
9
25.1
Hyundai Accent
28
37
2290
4
1.5
A
9
34.4
Explanation / Answer
Solution:-
State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.
Null hypothesis: PManual> PAuto
Alternative hypothesis: PManual < PAuto
Note that these hypotheses constitute a one-tailed test.
Formulate an analysis plan. For this analysis, the significance level is 0.05. The test method is a two-proportion z-test.
Analyze sample data. Using sample data, we calculate the pooled sample proportion (p) and the standard error (SE). Using those measures, we compute the z-score test statistic (z).
p = (p1 * n1 + p2 * n2) / (n1 + n2)
p = 0.50
SE = sqrt{ p * ( 1 - p ) * [ (1/n1) + (1/n2) ] }
SE = 0.1581
z = (p1 - p2) / SE
z = - 2.53
where p1 is the sample proportion in sample 1, where p2 is the sample proportion in sample 2, n1 is the size of sample 1, and n2 is the size of sample 2.
Since we have a one-tailed test, the P-value is the probability that the z-score is less than -2.53. We use the Normal Distribution Calculator to find P(z < -2.53) = 0.0057
Interpret results. Since the P-value (0.0057) is less than the significance level (0.05), we have to reject the null hypothesis.
From the above test we have sufficient evidence in the favor of the claim that automatic cars are more common than manual cars.
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