If a 95 confidence interval of an estimator of a regression

If a 95% confidence interval of an estimator of a regression coefficient beta contains 0, which of the following statements is true

1- The true value of beta is 0

2- the estimated value of beta is 0

3- The null hypothesis bet =0 cannot be rejected at alpha=0.5

4- None of the above

Solution

3- The null hypothesis bet =0 cannot be rejected at alpha=0.5

If the confidence interval contains 0 then there evidence suggests that beta can take value 0 too. Thus we fail to reject the null hypothesis.