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Interval Estimation for the Difference Between Two Proportions

This approach uses sample data to determine a range (interval) that, at an established level of confidence, will contain the difference between two population proportions.

Steps

Determine the confidence level (generally alpha .05)

Use the z distribution table to find the critical value for a 2-tailed test (at alpha .05 the critical value would equal 1.96)

Estimate Sampling Error

         

where                  and   

 

Estimate the Interval

CI = (p1-p2) (CV)(Sp1-p2)

p1-p2 = difference between two sample proportions

CV = critical value

 

Interpret

Based on alpha .05, you are 95% confident that the difference between the proportions of the two subgroups in the population from which the sample was obtained is between __ and __.

Note: Given the sample data and level of error, the confidence interval provides an estimated range of proportions that is most likely to contain the difference between the population subgroups. The term "most likely" is measured by alpha or in most cases there is a 5% chance (alpha .05) that the confidence interval does not contain the true difference between the subgroups in the population.


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