Question

In looking at the difference between two sample proportions or the difference between two sample means, why does one need independence between the two samples in order to construct confidence intervals for the difference or do a hypothesis test for the difference?

Answer 1

Question:at the difference between two sample proportions or the difference between two sample means, why does one need independence between the two samples in order to construct confidence intervals for the difference or do a hypothesis test for the difference?

Answer: Independence of sample means that sample values are selected from one population aren't related to sample value selected from other population.

While constructing confidence intervals for the difference our we want to prove that both the population means or proportions are significantly different.

If we consider dependent sample, then it may mislead our claim. More theoretically speaking our standard error will be increase because of std. error due to between sample values.

Hence considering dependent samples for difference of means or proportion is invalid.