CARS: A sample of 20 cars, including measurements of fuel consumption (city mi/g
ID: 3365839 • 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
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
4. Is there evidence that automatic cars are more common than manual cars?
i. 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
ii. 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
Question 4
Here hypothesises are
H0 : Manual cars are same popular as the automatic cars. p = 0.5
Ha : Automatic cars are more populaer than the automatic cars. p > 0.5
here p is the proportion of automatic cars in the population ad Manual cars and automatic cars are mutually exclusive in nature.
so Here sample proportion (point estimate)= Total number of automatic cars/ Total cars in sample = 14/20 = 0.7
here we can take assumption that data is normally distributed and sample is also derived from a population normally distrbuted.
Here standard error of the proportion se0 = sqrt (0.5 * 0.5 / 20) = 0.1118
Test statistic
Z = (0.7 - 0.5)/ 0.1118 = 1.789
so P - value = Pr(Z > 1.789) = 1 - Pr(Z < 1.789) = 1 - 0.9632 = 0.0368
(ii) here p - value is less than 0.05 significance level so we can conclude that automatic cars are more common than manual cars
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