SOLUTION: An automobile manufacturer collects mileage data for a sample of 9 cars in various weight categories by use of a standard grade of gasoline with and without a particular additive.

Question 1195184: An automobile manufacturer collects mileage data for a sample of 9 cars in various weight categories by use of a standard grade of gasoline with and without a particular additive. The Engines were tuned to the same specifications before each run, and the same drivers were used for the two gasoline conditions (with the driver in fact being unaware of which gasoline was being used on a particular run). The mileage data is given in the table below:
Automobile: 1,2,3,4,5,6,7,8,9
Mileage with Additive: 20.3, 36.5, 32.0, 29.3, 28.4, 25.7, 25.2, 22.6, 21.9
Mileage without Additive: 20.0, 35.9, 32.0, 29.6, 28.1, 25.5, 24.9, 22.0, 21.5
(a) Test whether the additive is effective in increasing the mileage at 10% level of significance.
(b) Do you think it is necessary to use the same drivers for two gasoline conditions? Explain your reasoning.

Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
d=difference from 0 with-without
Ho: d=0 no change
Ha: change
alpha =0.10 p{reject Ho|Ho true}
test is a 1 sample two-way t-test
critical value reject t if |t|>1.397
difference is 0.3,0.6,0,0,-0.3,0.3,0.2,0.3,0.6,0.4
mean is 0.2667
s=0.283
t=(0.2667)/0.283/sqrt(9)
=2.83
reject Ho: there is a change in mileage.p-value=0.022
Absolutely use the same drivers in the conditions, unless one can prove that there is no interaction. How one drives makes a big difference in mileage.

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