Question

IF the 95% confidence interval does not contains the hypothesised parameter, then a hypothesis test at the 0.05 level will almost always reject the null hypothesis in a two-tailed test? do you agree with this statement? explain.

Answer 1

First we will understand z value on a normal curve, a z value indicates how many standard deviations a point is from the mean

The below normal curve shows a 95% confidence region with two critical regions(two tailed test), the total area of the critical regions is 0.05(level of significance), the shaded region below shows the area of confidence for the Null hypothesis

The z values -1.96 and +1.96 are the critical values,  the hypothesised parameter Z_c we get should be in between these two values, so that the value lies in the confidence region(shown in the normal curve above) and the null hypothesis is not rejected . So we agree with the statement if the 95% confidence interval does not contains the hypothesised parameter, then a hypothesis test at the 0.05 level will almost always reject the null hypothesis in a two-tailed test.