Suppose chemical engineers wish to compare the fuel economy obtained by two different formulations of gasoline. Since fuel economy varies widely from car to car, if the mean fuel economy of two independent samples of vehicles run on the two types of fuel were compared, even if one formulation were better than the other, the large variability from vehicle to vehicle might make any difference arising from the difference in fuel difficult to detect. Instead of independent random samples, it would make more sense to select pairs of cars of the same make and model and driven under similar circumstances, and compare the fuel economy of the two cars in each pair. Thus, the data would look something as follows, where the first car in each pair is operation on one formulation of the fuel (call it Type 1 gasoline) and the second car is operated on the second (call it Type 2 gasoline). Make and Model Car 1 Car 2 Buick LaCrosse 17.0 17.0 Dodge Viper 13.2 12.9 Honda CR-Z 35.3 35.4 Hummer H 3 13.6 13.2 Lexus RX 32.7 32.5 Mazda CX-9 18.4 18.1 Saab 9-3 22.5 22.5 Toyota Corolla 26.8 26.7 Volvo XC 90 15.1 15.0 The first column of numbers form a sample from Population 1, the population of all cars operated on Type gasoline; the second column of numbers form a sample from Population 2, the population of all cars operated on Type 2 gasoline. The paired-observations differences are shown below. Make and Model Car 1 Car 2 Difference Buick LaCrosse 17.0 17.0 0.0 Dodge Viper 13.2 12.9 0.3 Honda CR-Z 35.3 35.4 -0.1 Hummer H 3 13.6 13.2 Lexus RX 32,7 32.5 0.2 Mazda CX-9 18.4 18.1 0.3 Saab 9-3 22.5 22.5 0.0 Toyota Corolla 26.8 26.7 0.1 Volvo XC 90 15.1 15.0 0.1 Let up = µ1 – M2. We consider testing the following hypotheses at a 0.05 level of significance. Ho : up = 0 versus H1 : µp > 0. The value of the test statistic equals (Give your answer precise to one decimal place, e.g., 3.1, -2.4, 1.0.) The reference distribution is the t-distribution with degrees of freedom. The relevant rejection region is bounded by (Write your answer precise to three decimal places, e.g., 1.108, 2.131.) The data sufficient evidence, at the 0.05 level of significance, to support the hypothesi that the mean fuel economy provided by Type 1 gasoline is greater than that for Type 2 gasoline. (Write "provide" or "do not provide".)

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Suppose chemical engineers wish to compare the fuel economy obtained by two different formulations of
gasoline.
Since fuel economy varies widely from car to car, if the mean fuel economy of two independent samples of
vehicles run on the two types of fuel were compared, even if one formulation were better than the other,
the large variability from vehicle to vehicle might make any difference arising from the difference in fuel
difficult to detect.
Instead of independent random samples, it would make more sense to select pairs of cars of the same make
and model and driven under similar circumstances, and compare the fuel economy of the two cars in each
pair.
Thus, the data would look something as follows, where the first car in each pair is operation on one
formulation of the fuel (call it Type 1 gasoline) and the second car is operated on the second (call it Type 2
gasoline).
Make and Model
Car 1
Car 2
Buick LaCrosse
17.0
17.0
Dodge Viper
13.2
12.9
Honda CR-Z
35.3
35.4
Hummer H 3
13.6
13.2
Lexus RX
32.7
32.5
Mazda CX-9
18.4
18.1
Saab 9-3
22.5
22.5
Toyota Corolla
26.8
26.7
Volvo XC 90
15.1
15.0
The first column of numbers form a sample from Population 1, the population of all cars operated on Type 1
gasoline; the second column of numbers form a sample from Population 2, the population of all cars
operated on Type 2 gasoline.
The paired-observations differences are shown below.
Make and Model
Car 1
Car 2
Difference
Buick LaCrosse
17.0
17.0
0.0
Dodge Viper
13.2
12.9
0.3
Honda CR-Z
35.3
35.4
-0.1
Hummer H 3
13.6
13.2
0.4
Lexus RX
32.7
32.5
0.2
Mazda CX-9
18.4
18.1
0.3
Saab 9-3
22.5
22.5
0.0
Toyota Corolla
26.8
26.7
0.1
Volvo XC 90
15.1
15.0
0.1
Let up = 41 – u2. We consider testing the following hypotheses at a 0.05 level of significance.
Ho : µp = 0 versus H1 : µp > 0.
The value of the test statistic equals
(Give your answer precise to one decimal place,
e.g., 3.1, -2.4, 1.0.)
The reference distribution is the t-distribution with
degrees of freedom.
The relevant rejection region is bounded by
(Write your answer precise to three
decimal places, e.g., 1.108, 2.131.)
The data
sufficient evidence, at the 0.05 level of significance, to support the hypothesis
that the mean fuel economy provided by Type 1 gasoline is greater than that for Type 2 gasoline. (Write
"provide" or "do not provide".)
Transcribed Image Text:Suppose chemical engineers wish to compare the fuel economy obtained by two different formulations of gasoline. Since fuel economy varies widely from car to car, if the mean fuel economy of two independent samples of vehicles run on the two types of fuel were compared, even if one formulation were better than the other, the large variability from vehicle to vehicle might make any difference arising from the difference in fuel difficult to detect. Instead of independent random samples, it would make more sense to select pairs of cars of the same make and model and driven under similar circumstances, and compare the fuel economy of the two cars in each pair. Thus, the data would look something as follows, where the first car in each pair is operation on one formulation of the fuel (call it Type 1 gasoline) and the second car is operated on the second (call it Type 2 gasoline). Make and Model Car 1 Car 2 Buick LaCrosse 17.0 17.0 Dodge Viper 13.2 12.9 Honda CR-Z 35.3 35.4 Hummer H 3 13.6 13.2 Lexus RX 32.7 32.5 Mazda CX-9 18.4 18.1 Saab 9-3 22.5 22.5 Toyota Corolla 26.8 26.7 Volvo XC 90 15.1 15.0 The first column of numbers form a sample from Population 1, the population of all cars operated on Type 1 gasoline; the second column of numbers form a sample from Population 2, the population of all cars operated on Type 2 gasoline. The paired-observations differences are shown below. Make and Model Car 1 Car 2 Difference Buick LaCrosse 17.0 17.0 0.0 Dodge Viper 13.2 12.9 0.3 Honda CR-Z 35.3 35.4 -0.1 Hummer H 3 13.6 13.2 0.4 Lexus RX 32.7 32.5 0.2 Mazda CX-9 18.4 18.1 0.3 Saab 9-3 22.5 22.5 0.0 Toyota Corolla 26.8 26.7 0.1 Volvo XC 90 15.1 15.0 0.1 Let up = 41 – u2. We consider testing the following hypotheses at a 0.05 level of significance. Ho : µp = 0 versus H1 : µp > 0. The value of the test statistic equals (Give your answer precise to one decimal place, e.g., 3.1, -2.4, 1.0.) The reference distribution is the t-distribution with degrees of freedom. The relevant rejection region is bounded by (Write your answer precise to three decimal places, e.g., 1.108, 2.131.) The data sufficient evidence, at the 0.05 level of significance, to support the hypothesis that the mean fuel economy provided by Type 1 gasoline is greater than that for Type 2 gasoline. (Write "provide" or "do not provide".)
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