Chapter 6 Section 2

There is a direct relationship between a two-sided test and a confidence interval; that is a if my confidence interval is 95%, then the corresponding significance level, α, is 1 –0.95 = 0.05. Thus, we can see that since p-value < 0.05, which would result in a rejection of the null hypothesis; we will reject the assumed μ value, 30. Now, lets see the logic here. The test of significance just rejected the null. If the 95% confidence interval contains the value of 30, it would be saying 30 is totally possible; 95% confident. This means the two tests would contradict each other. One would say, yes 30 is possible, the other would say the opposite. So no, 30 would not be found in the 95% confidence interval.