Confidence interval in two tailed t test If I am doing a two tailed $t$ test, i.e my null and alternate hypothesis are
$$H_0: \mu = 0$$
$$H_1: \mu \neq 0,$$
then would I choose and $\alpha$ value of $0.05$ for a $95$% confidence interval or a value of $0.025$?
EDIT: Also, will be degrees of freedom be $n - 2$ or $n - 1$?
 A: For a 95% confidence interval and a single test, by definition your significance ($\alpha$) is 5%.
However, this is not the same as the quantile(s) that you will use as a threshold, and I believe that is what is causing your confusion. You wish to chose the boundaries of the confidence interval such that there is only 5% chance of being outside that interval for values sampled according to that distribution. For a symmetric distribution (like the t distribution) and more importantly for a symmetric confidence interval, you pick them so that there is 2.5% chance of being to the left (smaller) of the interval and 2.5% chance of being to the right (larger). Thus, the confidence interval will be between the 2.5 percentile of that distribution and the 97.5 percentile.
A: This is a really good and easy to follow guide on Hypothesis Testing and Confidence intervals. The details and tangible real world explanations and analogies to business concepts where the use of t intervals and hypothesis would be beneficial. It covers independent and dependent testing, equal and unequal variance, large and small sample testing, confidence intervals. It's essentially a killer walk through of the basic concepts of confidence intervals and hypothesis testing.
https://www.kendallhunt.com/uploadedFiles/Kendall_Hunt/Content/Higher_Education/Uploads/CH09_%20Jones_Text.pdf
