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Test of Hypothesis for difference in proportions

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A random sample of 200 workers from Factory A showed that 130 were satisfied with their job. Another random sample of 125 workers from Factory B showed that 70 were satisfied with their job. Can it be concluded that the proportion of satisfied workers in Factory A is greater than in Factory B?
Formulate and test the appropriate hypotheses at the 1% level of significance

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Solution Summary

The solution formulates and tests the hypothesis that the proportion of satisfied workers in Factory A is greater than in Factory B.

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Null Hypothesis: H0: p1=p2
There is no difference between the proportion of satisfied workers of the two factories
Alternative Hypothesis: H1: p > p2
Proportion of satisfied workers in Factory A is greater than in Factory B

p=proportion satisfied with their jobs
n=sample size

Factory A
n1= 200
p1= 65% =130/200
q1=1-p1= 35%

Factory B
n2= 125
p2= 56% =70/125
q2=1-p2= 44%

difference= 9% =65%-56%

Best estimate of the overall proportion of success ...

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