Two different chemical formulations of rocket fuel are considered for the peak t

Question

Two different chemical formulations of rocket fuel are considered for the peak thrust they deliver in a particular design for a rocket engine. The thrust/weight ratios (in kilograms force per gram) for each of the two fuels are measured several times. The results are as follows:

Fuel A: 54.3 52.9 57.9 58.2 53.4 51.4 56.8 55.9 57.9 56.8 58.4 52.9 55.5 51.3 51.8 53.3

Fuel B: 55.1 55.5 53.1 50.5 49.7 50.1 52.4 54.4 54.1 55.6 56.1 54.8 48.4 48.3 55.5 54.7

a) If you want to construct a hypothesis test, state your null and alternative hypothesis.

b) Is the experiment a factorial balanced CR design?

c) What is the degree of freedom of treatment sum of square and error sum of square? If SSTrt and SSE is given: SSTrt=28.88 SSE=209.45, what is the value of your test statistics?

d) We get a p-value of 0.0509 and we have significance level 0.10 for this case, state your conclusion of the test.

Explanation / Answer

a) Hypothesis:

Null hypothesis:

There is no difference in mean thrust/weight ratio between fuel A and fuel B.

Alternative hypothesis:

There is a significant mean difference in thrust/weight raion between fuel A and fuel B

b)

The experiment has one factor with two levels and the number of replication is same in both the levels. Hence, the given experiment is CR design.

c)

Degrees of Freedom:

DF for treatment sum of squares = k - 1.

Where, k = Number of groups = 2

Therefore DF for treatment sum of squares = 2 - 1 =1

DF for Error Sum of Squares = N - k

N = Total number of observations = 32

Hence, the DF for error sum of squares = 32 - 2 = 30

Test statistic

Given:

SSTrt=28.88, SSE=209.45

Test statistic = Mean Sum of Squares of Treatment / Mean Sum of Squares of Error

Mean Sum of Squares of Treatment = Sum of Squares of Treatment / DF for treatment sum of squares

Mean Sum of Squares of Treatment = 28.88/1 = 28.88

Mean Sum of Squares of Error = SSE / DF for Error sum of squares

Mean Sum of Squares of Error = 209.45/30 = 6.9817

Therefore,

Test statistic = 28.88/6.9817 = 4.1365

d) Conclusion:

Given: p-value = 0.0509 and level of significance = 0.10

Since, the p-value is less than the level of significance of 0.10 we would reject the null hypothesis and conclude that there is a significant difference in the mean thrust/weight ratios between Fuel A and Fuel B at 10% level of significance.

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