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# Confidence interval for the difference of proportions

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After a certain candidate announced his intention for running for the premiership of a province, many polls were conducted to assess his chanced for success. Among them were two polls of independant samples taken from two populations. The poll in the first community interviewed 400 people and asked if the candidate had a chance of becoming the next premier. Out of this sample of 400, 192 people responded "yes". In the second community, 300 people were asked exactly the same question, and 108 answered "yes".
Develop a 90% confidence interval for the difference of proportions who answered "yes".

##### Solution Summary

Confidence interval for the difference of proportions is calculated in this solution.

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First population
p1= 0.48 =192/400 =proportion of those who say yes
q1=1-p= 0.52 = 1 - 0.48 =proportion of those who did not say yes
n1= 400

Second population
p2= 0.36 =108/300 =proportion of those who say yes
q2=1-p= 0.64 = 1 - 0.36 ...

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