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500 articles from a factory are examined and found to be 2% defective. 800 similar articles from a second factory are found to have only 1.5% defective. Can it reasonably be concluded that the
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Solution:

n1=500,n2=800

p1= proportion of defective from first factory =2%=0.02

p2= proportion of defective from second factory =1.5%=0.015

H0 : There is no significant difference between the two products i.e., the products do not differ in quality. H1:p1<p2 (one tailed test)  Under H0,z=p1p2PQ(1n1+1n2)P=n1p1+n2p2n1+n2=0.02(500)+(0.015)(800)500+800=0.01692;Q=1P=0.9830 z=0.020.0150.01692×0.983(1500+1800)=0.68

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Conclusion:

As, |z|<1.645, the significant value of z at 5% level of significance. H0 is accepted. i.e., the products do not differ in quality.

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