Please help in question a and b and show the formula and steps

Question

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 1

First, determine which test statistic you should use.

1.) You are being asked about differences over two occasions for the same participants. You will want a repeated measures statistic.

2.) A simple, repeated measures t test should do the trick.

3.) t = mean(difference score, time 2 - time 1)/(standard deviation of the differences scores/sqrt(N difference scores)