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ANOVA Study on Egg Housing Systems

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A study of four different types of egg housing systems was performed. The four egg housing systems were cage, barn, free range, and organic. In addition to housing system, the researchers also determined the weight class (medium or large) for each sampled egg. The data on whipping capacity
(percent overrun) for the 28 sampled eggs are shown in the accompanying table and saved in the EGGS file. The researchers want to investigate the effect of both housing system and weight class on the mean whipping capacity of the eggs. In particular, they want to know whether the difference
between the mean whipping capacity of medium and large eggs depends on the housing system.
See attached excel document for data

Conduct an ANOVA on the data. Report the results in an ANOVA table.

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Solution Summary

A research work on eggs whipping capacity vs housing system

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For mean values (X_bar), see attachment.
XT_bar = 504.86 (X total mean)

Degree of freedom & Sum of squares:

Degree of freedom for weight class (dfA) = 2 -1 = 1
SSA = sum(bn(XA_bar - XT_bar)^2) = (5+3+3+3)*(501.57-504.86)^2 + (5+3+3+3)*(508.14-504.86)^2 = 302.16
MSA = SSA/dfA = 302.16

Degree of freedom for egg housing (dfB)= 4 -1 = 3
SSB = sum(an*(XA_bar - XT_bar)^2) = 2*5*(479.7-504.86)^2+2*3*(516.17-504.86)^2+2*3*(511.84-504.86)^2+2*3*(528.5-504.86)^2 = ...

Solution provided by:
  • BEng, Allahabad University, India
  • MSc , Pune University, India
  • PhD (IP), Pune University, India
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