Question

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:

		H0: There is an association between the factory and the quality of the parts HA: There is no association between the factory and the quality of the parts
		H0: There is no association between the factory and the quality of the parts HA: There is an association between the factory and the quality of the parts
		Let pA, pB, and pC be the true proportion of defective parts from factories A, B, and C, respectively. H0: pA = pB = pC HA: pA ≠ pB ≠ pC
		Let pA, pB, and pC be the true proportion of defective parts from factories A, B, and C, respectively. H0: pA ≠ pB ≠ pC HA: pA = pB = pC

Answer 1

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, p​​​​​​i and q​​​​​​i denote the proportion of defective and non defective in the lot from ith factory,. p​​​​​​i + q​​​​​​i = 1.

Then the null hypothesis and alternative hypothesis will be :

H​​​​​0 : pA=pB=pC

H​​​​​​A : pA pBpC

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