Using the $C$% confidence interval for $\mu$ to perform two sided one sample $ t$ test: full explanation
If $\mu_0$ is not in the $C$% confidence interval, the sample mean is significantly different from $\mu_0$ at significance level $\alpha = 1  C/100$
If $\mu_0$ is not in the $C$% confidence interval, the sample mean is significantly different from $\mu_0$ at significance level $\alpha = 1  C/100$. In order to understand why, we have to be aware of the following three points, which are illustrated in the figure above:
