Statistics For Dummies -
“95% CI” means that if we repeated the sampling process many times, 95% of those intervals would contain the true $\mu$. Not “probability that $\mu$ lies in this interval” — $\mu$ is fixed, interval is random.
For population mean $\mu$: $$\barx \pm t^* \cdot \fracs\sqrtn$$
For a sample mean: $$t = \frac\barx - \mu_0s / \sqrtn$$
“95% CI” means that if we repeated the sampling process many times, 95% of those intervals would contain the true $\mu$. Not “probability that $\mu$ lies in this interval” — $\mu$ is fixed, interval is random.
For population mean $\mu$: $$\barx \pm t^* \cdot \fracs\sqrtn$$
For a sample mean: $$t = \frac\barx - \mu_0s / \sqrtn$$