A test of Ho:mu=7 versus Ha:mu=/=7 does not reject the null hypothesis at the 5% level. If calculated using the same sample data, which of the following is a possible 95% confidence interval for the population mean?
8.4+/-1.1
9.2+/-3.4
6.2+/-0.5
8.4+/-0.9

Question

A test of Ho:mu=7 versus Ha:mu=/=7 does not reject the null hypothesis at the 5% level. If calculated using the same sample data, which of the following is a possible 95%  confidence interval for the population mean?
8.4+/-1.1
9.2+/-3.4
6.2+/-0.5
8.4+/-0.9

kirbykirby · Answer

If you don't reject the null, then there is evidence to think that the null hypothesis Ho is true. Thus, you have $H_0: \mu=7$, so the most likely confidence interval should be one in which 7 is found IN your confidence interval. 

If you look at all your choices, you will see that only one of the choices contains 7 in the interval. For example, the first interval $8.4 \pm 1.1 =(7.3, 9.5)$ does not contain 7.