An article in Lubrication Engineering (December 1990) described the results of a

Question

An article in Lubrication Engineering (December 1990) described the results of an experiment designed to investigate the effects of carbon material properties on the progression of blisters on carbon face seals. The carbon face seals are used extensively in equipment such as air turbine starters. Four different carbon materials were tested, and the surface roughness was measured. The data and Excel output are as follows: Carbon Material Surface Roughness Type EC10 EC10A EC4 EC1 0.5 0.31 0.2 0.1 0.55 0.22 0.28 0.16 0.55 0.25 0.22 0.18 0.54 0.24 0.28 0.1 0.45 0.28 0.25 0.16 ANOVA Source of Variation Between Groups Within Groups MS P-valueF 0.38658 0.0232 3 0.12886 88.86897 3.4342E-10 3.238872 160.00145 Total 0.40978 19 Determine if the carbon material type significantly affects surface roughness. a) What topic is this problem about? b) What are the treatments? Are they in rows or columns? c) What are the null and alternative hypotheses, in words? d) What Excel output will you need to use to determine the conclusion to your hypothesis test?

Explanation / Answer

Ans:

a)Here,we want to test whether mean surface roughness is same for all treatments(carbon material type)

b)Treatments are types of carbon material

Treatments are in rows(EC10,EC10A,EC4,EC1)

c)

Null hypothesis:

H0: mean surface roughness is same for four type of carbon material.

Ha:Atleast one of the mean roughness is different from others.

d)

Test statistic:

F=88.869

F critical=3.239

As,F=88.869>3.239,we reject null hypothesis.

We can conclude that atleast one of the mean roughness is different from others(or carbon material type significantly affects the surface roughness)

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