Suppose a random sample of parts from three different factories was collected and tested for faults, with the results summarised in the table below:
Factory A 
Factory B 
Factory C 
Total 

Defective 
18 
14 
23 
55 
Not Defective 
222 
226 
217 
665 
Total 
240 
240 
240 
720 
To test for a relationship between the factory and the quality of the parts (defective or not defective), the appropriate null and alternative hypotheses are:
H_{0}: There is an association between the factory and the quality of the parts H_{A}: There is no association between the factory and the quality of the parts 

H_{0}: There is no association between the factory and the quality of the parts H_{A}: There is an association between the factory and the quality of the parts 

Let p_{A}, p_{B}, and p_{C} be the true proportion of defective parts from factories A, B, and C, respectively. H_{0}: p_{A} = p_{B} = p_{C} H_{A}: p_{A} ≠ p_{B} ≠ p_{C} 

Let p_{A}, p_{B}, and p_{C} be the true proportion of defective parts from factories A, B, and C, respectively. H_{0}: p_{A} ≠ p_{B} ≠ p_{C} H_{A}: p_{A} = p_{B} = p_{C} 
This is a problem of testing the homogeneity of 3 populations Factory A, Factory B and Factory C, each having two classes  defective and non defective.
Let, pi and qi denote the proportion of defective and non defective in the lot from ith factory,. pi + qi = 1.
Then the null hypothesis and alternative hypothesis will be :
H0 : pA=pB=pC
HA : pA ￼pBpC
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