Identify each of the following statements as

Let's identify each of the statements as true or false in relation to confidence intervals (CIs):
A 95% CI is a numerical interval within which we are 95% confident that the true mean $\mu$ lies.
This statement is true. A 95% confidence interval means that if we were to repeat the same experiment multiple times, the true population mean $\mu$ would lie within the interval in 95% of those repetitions.
A 95% CI is a numerical interval within which we are 95% confident that the sample mean $\overline{x}$ lies.
This statement is also true. A 95% confidence interval for the sample mean $\overline{x}$ means that if we were to take multiple samples of the same size from the same population and calculate the sample mean $\overline{x}$ and the corresponding 95% confidence interval for each sample, then 95% of those intervals would contain the true population mean $\mu$.
The true mean $\mu$ is always inside the corresponding confidence interval.
This statement is false. While it is true that the true population mean $\mu$ is expected to be inside the confidence interval in most cases, it is not guaranteed to be inside the interval for any particular sample or experiment.
For a sample size $n=29$, the number of degrees of freedom is $n-1=28$.
This statement is true. The number of degrees of freedom for a t-distribution is equal to $n-1$, where $n$ is the sample size.
If we repeat an experiment 100 times (with 100 different samples) and construct a 95% CI each time, then approximately 5 of those 100 CIs would not contain the true mean $\mu$.
This statement is also true. The 95% confidence level means that in the long run, 95% of the intervals will contain the true population mean $\mu$, and approximately 5% will not. Therefore, if we construct 100 confidence intervals, we would expect approximately 5 of them to not contain the true population mean $\mu$.