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I have a question. I am confused because of a question I've seen. The question is as follows:

Hey guys! I am practicing confidence intervals in my statistics class and this problem stumped me:

"Listed below are the recent annual compensation amounts (in thousands of dollars) for a random sample of chief executive officers. The mean is 12,898 (thousand dollars) and the standard deviation is 7719(thousand dollars). Construct a 95% confidence interval estimate of the mean of the population of all such chief executive officers.

17,688 0.001 19,629 12,408 14,765

I know that I need to check the t-table, because: no population standard deviation is given... I also know that the degrees of freedom is 4 and practically, I know the formula as well...

The problem is that question keeps confusing me. I mean: how do I know whether this is a one-tailed test or a two-tailed test? Is this even possible when getting the confidence interval? I am also confused because the formula says: Z a/2, so does that mean it's ALWAYS a two-tailed test, no matter what?

I would love a good explanation of it. I don't need the answer of the question itself... it's the logic behind it I want to understand.

kjetil b halvorsen
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Siyah
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  • Your question is puzzling because the quoted problem doesn't concern testing at all, nor does it even mention testing. It asks merely to construct a *confidence interval*. By definition, an "interval" has two endpoints, both of which you need to compute. (Contrast this to a *confidence limit* which has just one endpoint.) – whuber Dec 13 '16 at 16:00
  • I get that, but... when I need to check the t-score table, I need to find out the confidence interval I am using. If it's 95% as stated... it's 0.05 and I get a number. If it's 95% (0.05) / 2 (because two tailed), I'd get 0.025 and that's different... – Siyah Dec 13 '16 at 16:01
  • Maybe http://stats.stackexchange.com/questions/19195 will help. If not, then please [search our site](http://stats.stackexchange.com/search?q=two+tailed+half). It comes down to this: when you exclude 2.5% from each end of an interval, then you are left with 95%. – whuber Dec 13 '16 at 17:33
  • One-tailed or two-tailed is a decision made by either the question or the statistician. In the former case, one-tailed is often indicated by the presence of words like *greater than* or *less than*. If there is no word in the question indicating a direction to the possible difference in values, it's probably a two-tailed test. In the latter case, if the statistician decides on a one-or two-tailed test, the statistician is making a strong statement about the (presumed) relationships the data describes. – Upper_Case Dec 13 '16 at 17:54
  • But as whuber wrote, that's not quite on-topic for what you are describing. Confidence interval, t-test, and one- or two-tailed are all terms that will lead to a lot of confusion for you if used imprecisely, as is the case in the OP. – Upper_Case Dec 13 '16 at 17:58

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