An experiment was performed to judge the effect of four different fuels and thre

Question

An experiment was performed to judge the effect of four different fuels and three different tyoes of launchers on the range of certain rocket. Test, on the basis of the following ranges in miles, whether there is a significant effect due to difference in fuels and whether there is a significant effect due to difference in launchers:

Use the 0.01 level of significance.

Please describe how to choose block and treatment and why?

Fuel 1Fuel 2 Launcher X45.957.652.241.7 Launcher Y46.051.0 50.138.8 Launcher Z 45.756.9. 55.3 48.1 Fuel 3 Fuel 4

Explanation / Answer

Here, we shall use Excel and R programming to solve this problem.
Firstly, we store the data in Excel in such a way so that we are able to load and analyse it on R.
We store the data in the following way.

We are to use alpha = 0.01 as the level of significance while checking for the significant effects due to the difference in fuels and the difference in launchers in the ANOVA table. The R-code of the ANOVA test is as given below.

# LOADING DATA INTO THE SYSTEM
data=read.csv("C:\Users\DESKTOP\Desktop\a.csv")
data
attach(data)

# TWO WAY ANOVA
res=aov(range ~ launcher + fuel, data)
summary(res)

From the ANOVA results, we can conclude the following, based on the p-values and a significance level of 0.01:

Now, we know that blocking is a partition of the experimental units into groups, known as blocks, such that units in the same block are as similar as possible. Consequently, variation between units in the same block should be small in comparison with variation between units in different blocks.
Also, randomization is the random allocation of the experimental units to the treatments in order to avoid biasing the results through any extraneous factors which might be present.

In this data or in any other data, we assign the experimental units to groups such that they are heterogenous across groups and homogenous within groups. Here, groups or blocks that we have used are in the launcher variable where range of rockets from different launchers are measured.
While choosing treatments, we choose those "processes" which are applied on experimental units in order to achieve a certain value. Here, that work is done by the fuel variable, where different types of fuels are used in order to arrive at the values of the range of rockets.

range launcher fuel 45.9 launcher X fuel 1 57.6 launcher X fuel 2 52.2 launcher X fuel 3 41.7 launcher X fuel 4 46 launcher Y fuel 1 51 launcher Y fuel 2 50.1 launcher Y fuel 3 38.8 launcher Y fuel 4 45.7 launcher Z fuel 1 56.9 launcher Z fuel 2 55.3 launcher Z fuel 3 48.1 launcher Z fuel 4

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