Confidence Interval on the Difference Between Proportions (2 of 4)

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Therefore the proportions who solve the problem are 0.65 for the psychology majors (p₁) and 0.41 for the physics majors (p₂). The goal of the experiment is to estimate the difference between the proportion of psychology majors in the population that can solve the problem (π₁) and the proportion of physics majors in the population that can solve it ( π₂). The statistic p₁ - p₂ is used as an estimate of π₁ - π₂. In this experiment, the estimated value of π₁ - π₂ is 0.65 - 0.41 = 0.24.

To compute the confidence interval, the standard error of p₁- p₂ is needed. The standard error is:



The estimated standard error is:



= 0.067