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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 $n - 1$?

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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.

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  • $\begingroup$ So how do I word this? Am I still going to have my $\alpha$ value as 0.025 or would I need to change it to 0.05? Also, do you know anything about my edit? $\endgroup$
    – Kaish
    Apr 17, 2013 at 14:39
  • $\begingroup$ $\alpha$ stays 5%, as per my first sentence. In many formulas regarding confidence intervals, you will find quantiles denoted $t_{\alpha/2}$, matching my explanation above, but that doesn't change $\alpha$ itself. Regarding the edit: whether you use a onesided or twosided test has no influence whatsoever on your degrees of freedom (this makes sense, as this would change the distribution itself). $\endgroup$
    – Nick Sabbe
    Apr 17, 2013 at 14:46
  • $\begingroup$ Ok thank you. Do you know what the degrees of freedom are for this test? It is a t test with unequal variances. $\endgroup$
    – Kaish
    Apr 17, 2013 at 14:57
  • $\begingroup$ For the degrees of freedom: find whatever you need at the relevant Wikipedia page (just scroll down towards unequal variances). $\endgroup$
    – Nick Sabbe
    Apr 17, 2013 at 15:37
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    $\begingroup$ @Kaish Are you sure the table is giving you $\alpha$'s rather than upper tail areas? $\endgroup$
    – Glen_b
    Apr 17, 2013 at 23:18
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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

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  • $\begingroup$ Can you please elaborate on the answer? Link-only answers are generally discouraged. $\endgroup$
    – Dawny33
    Nov 19, 2015 at 6:05

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