Sampling Distribution of the Difference Between Two Proportions (2 of 2)

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For this example, the mean of the sampling distribution of p₁ - p₂ is:

μ= π₁ - π₂ = 0.8 - 0.4 = 0.4.

The standard error is:



= 0 .133.

The solution to the problem is the probability that p₁ - p₂ is less than or equal to 0. The number of standard deviations above the mean associated with a difference in proportions of 0 is:



From z table it can be determined that only 0.0013 of the time would p₁ - p₂ be 3.01 or more standard deviations below the mean.

Next chapter: Point estimation