# Test of Hypothesis for difference in proportions

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

https://brainmass.com/statistics/hypothesis-testing/16450

#### Solution Preview

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 ...

#### Solution Summary

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