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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 X 1 and X 2 as given in the table. Consequently, D = X 1 -X 2 .
-Compute the standard deviation of the differences.
A) 0.84
B) 0.78
C) 0.13
D) 0.11

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Use the following to answer questions 
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 X 1 and X 2 as given in the table. Consequently, D = X 1 -X 2 . 
-Compute the standard deviation of the differences.
A) 0.84 
B) 0.78 
C) 0.13 
D) 0.11

Quizplus · Accepted Answer

To compute the standard deviation of the differences, we need to first calculate the sample mean of the differences, which is -0.5. Then, we calculate the sum of the squared differences from the mean, which is 1.25. Finally, we divide by n-1=6 and take the square root to get the standard deviation of the differences, which is approximately 0.78. Therefore, the correct choice is B.

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