Question

In what type of equations is it ok for a significance test and a confidence interval not agree?

Answer choices: one mean, mean of matched pairs difference, difference of two independent means, one proportion, difference of two independent proportions, and McNemar's test

This is really my own stats question I'm just kind of confused on when it matters.

Answer 1

Generally a significance test (using a p-value) and a test through constructing coincidence interval(i.e to check if the confidence interval contains the true parameter or not) should theoretically agree. however if the underlying distribution is not symmetric , p-value for testing two sided alternatives may not be defined properly. In the above question, all the test statistics but that of Mcnemar's test has symmetric distribution. But the Mcnemar's test statistic follows a chi-square distribution Which is not symmetric.. So in that case, if we attempt to check two sided alternatives, significance test and confidence interval may not match..