The mean of the sampling distribution of the difference between sample proportions,
₁ -
₂,is equal to the difference between the corresponding population proportions,P₁ - P₂.

Question

The mean of the sampling distribution of the difference between sample proportions, ₁ - ₂,is equal to the difference between the corresponding population proportions,P₁ - P₂.

Quizplus · Accepted Answer

This is true because the mean of the sampling distribution of the difference between sample proportions is equal to the difference between the corresponding population proportions. This is known as the central limit theorem, which states that as sample size increases, the sampling distribution of the mean or difference between proportions becomes approximately normal with a mean equal to the population mean and a standard deviation equal to the population standard deviation divided by the square root of the sample size. Therefore, if we have a large enough sample size, we can estimate the population proportion using the sample proportion and compute the difference between two sample proportions to test for a significant difference between two populations.

The Mean of the Sampling Distribution of the Difference Between