Question

We are often interested in whether the confidence interval estimate contains 0. What can we say about the population mean µ1 compared to the population mean µ2 if the confidence interval includes 0, is entirely positive, and the is entirely negative?

Answer 1

When we do a testing of hypothesis our Null Hypothesis H0: . Based on the p value or the critical value, we take the decision of either rejecting the Null hypothesis or fail to reject the null hypothesis.

When we fail to reject the null, it means, there could have been a possibility where .

When we have a confidence interval, If the confidence interval contains 0, which means the limits will have 2 different signs, it means that it could be possible that , or simply that , in which case we fail to reject the null, or the test results are not statistically significant.

If both the limits are positive, then the interval does not contain 0, which means at no point , and therefore we would reject the null hypothesis or we say the results are statistically significant. It would also mean that , which is why the both limits are positive.

If both limits are negative, again 0 cannot be part of the interval and hence we would reject the null and conclude that the results are statistically significant. in this case , which is why both the limits are negative.