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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 the best way to organize the 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 types of gasoline in the same order. Then change to $4000$ pounds and do the three types of gasoline in order again.

(c) Choose gasoline at random, and run the car with this gasoline at $3000,3500,$ and $4000$ pounds in order. Choose one of the two remaining types of gasoline 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.

Step by step solution

01

Given information

There are nine combinations of weight and gasoline.

02

Concept

A simple random sample (SRS) of size $n$ is made up of $n$ people chosen from the population with an equal chance of being the sample that is actually chosen.

03

Explanation

There are nine different weight and gasoline combinations. Because no randomization is used, if we provide one treatment first and then another, we will end up with a systematic error. Given a variety of options: Systematic errors, such as car warming up, are introduced by choices $A,B,$ and $C,D$ and Videos do not provide an evenly distributed set of tests. As a result, the ideal method to organize the research is to: There are nine different weight and gasoline combinations. Run the automobile through each of these combinations multiple times. Make each of these runs in a different order.

Option (d) is thus correct.

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