Question

when you have two independent populations, explain the similarities and differences between the test of hypothesis for the difference between the means and the confidence interval estimate for the difference between the means?

Answer 1

Similarity is that the test statistic used to construct test of hypothesis and confidence intervals are same. And rejection decision would be same using either testing or confidence intervals concepts.

But differences occur in the sense that testing of hypothesis has more flexibility of looking into power of the test also, which we cannot have using confidence intervals, power plays important role in taking decisions regarding accepting or rejecting null hypothesis.