Question

You are planning an experiment to determine the effect of the brand of gasoline and the weight of a car on gas mileage measured in miles per gallon. You will use a single test car, adding weights so that its total weight is $3000,3500,$ or $4000$pounds. The car will drive on a test track at each weight using each of Amoco, Marathon, and Speedway gasoline. Which is best way to organize study ?

a. Start with $3000$ pounds and Amoco and run the car on the test track. Then do $3500$ and $4000$ pounds. Change to Marathon and go through the three weights in order. Then change to Speedway and do the three weights in order once more.

b. Start with$3000$pounds and Amoco and run the car on the test track. Then change to Marathon and then to Speedway without changing the weight. Then add weights to get $3500$pounds and go through the three gasolines in the same order. Then change to$4000$ pounds and do the three gasolines in order again.

c. Choose a gasoline at random, and run the car with this gasoline at $3000,3500$, and $4000$pounds in order. Choose one of the two remaining gasolines at random and again run the car at$3000,$ then $3500$, then $4000$ pounds. Do the same with the last gasoline.

d. There are nine combinations of weight and gasoline. Run the car several times using each of these combinations. Make all these runs in random order.

e. Randomly select an amount of weight and a brand of gasoline, and run the car on the test track. Repeat this process a total of 30 times.

Short answer

The best way to organize the study is (d) There are nine combinations of weight and gasoline. Run the car several times using each of these combinations. Make all these runs in random order.

Step-by-step solution

Given information 

We need to find Which is best way to organize study .

Explanation for correct statement (d)

Here , in this case we have to determine the effect of the brand of gasoline and the weight of a car on gas mileage measured in miles per gallon . As there are different categories for weights of car and also different gasoline such as Amoco, Marathon, and Speedway gasoline . So effect can only be studied by using below way of organizing -

There are nine combinations of weight and gasoline. Run the car several times using each of these combinations. Make all these runs in random order is true

Explanation for incorrect statement (a)

Here , different categories and permutations are not fulfilled.

So , The statement - Start with $3000$ pounds and Amoco and run the car on the test track. Then do$3500$ and $4000$ pounds. Change to Marathon and go through the three weights in order. Then change to Speedway and do the three weights in order once more is false

Explanation for incorrect statement (b)

Here , different categories and permutations are not fulfilled.

All options are not tested.

Explanation for incorrect statement (c)

Here , different categories and permutations are not fulfilled.

All options are not tested.

Explanation for incorrect statement (e)

Random selection will not give best way of organizing .