Test whether the type of gasoline used and the type of autompbile driven have any effect on gasoline consumption. Two types of gasoline, regular and high-octane, will be used, and two types of automobiles, two-wheel- and four-wheel drive, will be used in each group. There will be two automobiles in each group, for a total of eight automobiles used. Using a two-way analysis of variance, you need to perform the following steps. Show your answers in detailed manner. a. State the hypotheses. b. Find the critical value for each F test, using a = 0.05. c. Complete the summary table to get the test value. d. Make the decision. e. Summarize the results. The data (in miles per gallon) are shown here, and the summary table is given in Table 1. Type of automobile Gas Two-wheel-drive Four-wheel-drive Regular 26.7 28.6 25.2 29.3 High-octane 32.3 26.1 32.8 24.2 Table 1: ANOVA Summary Table Source SS d.f. MS F Gasoline A Automobile B Interaction (A × B) Within (error) 3.920 9.680 54.080 3.300 Total 70.980

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Test whether the type of gasoline used and the type of automobile driven have any effect on
gasoline consumption. Two types of gasoline, regular and high-octane, will be used, and two
types of automobiles, two-wheel- and four-wheel drive, will be used in each group. There will
be two automobiles in each group, for a total of eight automobiles used. Using a two-way
analysis of variance, you need to perform the following steps. Show your answers in detailed
manner.
a. State the hypotheses.
b. Find the critical value for each F test, using a = 0.05.
c. Complete the summary table to get the test value.
d. Make the decision.
e. Summarize the results.
The data (in miles per gallon) are shown here, and the summary table is given in Table 1.
Type of automobile
Gas
Two-wheel-drive
Four-wheel-drive
Regular
26.7
28.6
25.2
29.3
High-octane
32.3
26.1
32.8
24.2
Table 1: ANOVA Summary Table
Source
SS
d.f.
MS
F
Gasoline A
3.920
Automobile B
9.680
Interaction (A × B)
Within (error)
54.080
3.300
Total
70.980
Transcribed Image Text:Test whether the type of gasoline used and the type of automobile driven have any effect on gasoline consumption. Two types of gasoline, regular and high-octane, will be used, and two types of automobiles, two-wheel- and four-wheel drive, will be used in each group. There will be two automobiles in each group, for a total of eight automobiles used. Using a two-way analysis of variance, you need to perform the following steps. Show your answers in detailed manner. a. State the hypotheses. b. Find the critical value for each F test, using a = 0.05. c. Complete the summary table to get the test value. d. Make the decision. e. Summarize the results. The data (in miles per gallon) are shown here, and the summary table is given in Table 1. Type of automobile Gas Two-wheel-drive Four-wheel-drive Regular 26.7 28.6 25.2 29.3 High-octane 32.3 26.1 32.8 24.2 Table 1: ANOVA Summary Table Source SS d.f. MS F Gasoline A 3.920 Automobile B 9.680 Interaction (A × B) Within (error) 54.080 3.300 Total 70.980
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