A researcher wanted to determine if using an octane booster

A researcher wanted to determine if using an octane booster would
increase gasoline mileage. A random sample of seven cars was selected; the cars were driven for two weeks without the booster and two weeks with the booster. Use the definitions of X1 and X2 as given in the table.
Take d= X1 – X2 = Without booster – With booster.

X1 =mileage without booster X2 =mileage with booster d= X1- X2 d2 =( X1- X2)2
21.2 23.8
25.4 25.6
20.9 22.4
27.6 28.3
22.8 24.5
27.3 28.8
23.4 25.2
Σd = Σd2 =
d‾ =
22. State the Alternative Hypothesis
A)
B)
C)
D)
E) None of the above
23. Compute the mean of the differences
A) -1.67
B) 6.3
C) 1.67
D) -1.43
E) None of the above
24. Compute the standard deviation of the differences
A) 0.84
B) 0.78
C) 0.13
D) 0.11
E) None of the above
25. Determine the test statistic
A) 4.85
B) 1.943
C) -3.96
D) -4.85.
E) None of the above
26. What is the p-value?
A) 0.0028.
B) 0.0014.
C) 0.0009
D) 0.0001
E) None of the above
27. At α = 0.05 the correct decision and conclusion are
A) Reject H0, Booster does not increase mileage
B) Reject H0, Booster increases mileage
C) Fail to reject H0, Booster does not increase mileage
D) Fail to reject H0, Booster increases mileage
E) None of the above

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