Question

A researcher is interested in an experiment in which the fue consumption of buses is to be examined. The treatment factor to be considered is the effec of tire pressure on fuel consumption. Four different tire pressures (levels) are to be tested, A,B,C, and D. She designs the experiment by putting 1 gallon of gas in a bus and measure the number of miles per gallon. The resources she has are 16 gallons of gas and 16 buses each bus is used only one time. The researcher believes that the buses variability my affect the fuel consumption. So, she added the bus as a nuisance factor to the experiment that is described in scenario 01 . Four buses and 16 gallons of gas are available.

Answer 1

From the provided information, we understand that the researcher has four different types of tire pressures (A, B, C, and D) to experiment with and a total of 16 resources (composed of 16 buses and 16 gallons of gas).

The first step is to determine the total number of experiments to be conducted. As each bus is used only once, and we have four different tire pressures, we divide the total resources by the number of different pressures. This way, we ensure each tire pressure is tested the same number of times to maintain the validity of the experiment and control nuisance factors.

By doing so, we find that a total of 4 experiments will be conducted for each tire pressure level (16 resources / 4 pressure levels).

Next, we want to calculate the number of permutations, that is, the number of ways we can assign these four different pressures to our available resources. In mathematical terms, we want to determine the number of ways we can arrange the 4 pressure levels (A, B, C, and D) among the 16 buses.

This is achieved by calculating permutations, which is given by the formula:

Permutations = nPr = n! / (n - r)!

where:
n = number of total objects (in this case, our resources - buses and gallons of gas)
r = number of objects to choose from these (the number of tire pressure levels)

Substituting n = 16 and r = 4 in the formula, we get:

Permutations = 16! / (16-4)!
Through this calculation, we find that there are 43,680 different ways we can assign the four different tire pressures to the buses.

So, with 16 buses, 16 gallons of gas and 4 different tire pressures to test, the researcher will conduct a total of 4 experiments per pressure level and has indeed 43,680 ways to assign the different tire pressures.