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I'm currently beginning my studies in statistics and all of the examples of confidence interval questions I studied used (let's assume a 95% confidence interval) as a z formula z = 1 - (0.05/2), which would result in 0.975 and then using a z-table in 1.96. The thing is, is the alpha always divided by 2 or are all the examples I studied using a two sided distribution?

Caldass_
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Yes, it is because you're doing two-sided testing.

When you do two-sided testing, you have to allocate probability to both tails. You pick $0.975$ because $2.5\%$ goes up high, and $2.5\%$ goes down low.

Dave
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  • You're saying that there will be situations where the confidence interval actually is not two-sided? Can you please give me a link to an example or something? I could only find confidence intervals examples where z = 1 - (alpha/2). I thought it was because since there's a lower and upper limit in a confidence interval, you always divided the alpha by 2. So a 95% confidence interval would always have a Z-value of 1.96. – Caldass_ Jul 23 '20 at 22:05
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    https://stats.stackexchange.com/questions/257526/can-one-sided-confidence-intervals-have-95-coverage – Dave Jul 23 '20 at 22:11
  • Thank you! This was really helpful! Don't now if you use python, but do you have any idea why any of the confidence interval packages and metrics don't allow us to choose whether it is one-sided or two-sided? Somes examples: https://www.statsmodels.org/stable/generated/statsmodels.regression.linear_model.OLSResults.conf_int.html and scipy.stats.norm.interval() – Caldass_ Jul 24 '20 at 11:30
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    Two-sided confidence intervals are so much more common. If you find yourself in a situation where you want one-sided intervals, think hard about of one-sided intervals really are appropriate, and if they are, you can calculate them with your own function or method. I’m surprised that statsmodels doesn’t even allow for that in their method, however. – Dave Jul 24 '20 at 11:32