Problem:
To assess the effect of three different gasoline supplements on average mileage (mi/gal), researchers conducted an experiment using 60 automobiles of the same type, model, and engine size, with 10 automobiles randomly assigned to each gasoline blend. The six gasoline blends and the resulting data appear in the accompanying table.
|
Group
|
Description
|
ni
|
Sample Mean
|
Sample S.D.
|
|
1
|
Control
|
10
|
25.5999
|
5.59255
|
|
2
|
Control + Supplement A
|
10
|
26.7061
|
5.13037
|
|
3
|
Control + Supplement B
|
10
|
28.2070
|
4.00454
|
|
4
|
Control + Supplement C
|
10
|
33.2476
|
4.50070
|
|
5
|
Control + Supplement A + Supplement B
|
10
|
34.1239
|
5.80158
|
|
6
|
Control + Supplement A + Supplement C
|
10
|
37.3222
|
4.88503
|
Note: Because of the chemical makeup of supplement B and C, they could not be combined in the same blend.
a. Suppose you want to determine if there is an overall supplement A effect. Define a linear combination for this effect and calculate a 98% confidence interval for the linear combination.