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Confidence Intervals: tdistribution or normal distribution? 
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#1
Oct1910, 03:46 AM

P: 14

Hi all,
When working out confidence intervals based on population samples are you supposed to always use tdistributions, standard normal (z) distributions, or do you make a choice based on the sample size? Up until now I've been lucky enough to have large sample sizes (for some work I'm doing) so have been using the zdistribution. However I now have some data sets which range from n=1 (lol) to n=29 so am not sure if I should now be using tdistributions to define confidence intervals, or how I'd make that decision (e.g. use tdistribution if n<30, for example?) Thanks Rob 


#2
Oct2210, 08:32 AM

P: 2,499




#3
Oct2210, 10:42 AM

HW Helper
P: 1,361

Actually the notion of using the sample size as the determining factor is being (as it should be) tossed out. It is a remnant of the days before computing power was so readily available.
IF the assumption of normality can be made, when you know [tex] \sigma [/tex] (population standard deviation) use the Zinterval. When you don't know sigma (so you have only the sample standard deviation) use the tinterval. If your data is badly skewed, it is debatable whether the mean is the appropriate parameter to measure central tendency. 


#4
Oct2210, 04:48 PM

P: 2,499

Confidence Intervals: tdistribution or normal distribution?
What you say makes sense. Would you use the Z value for very small samples, say n=5, if you did know sigma? EDIT: In most of my experience sigma is not known. 


#5
Oct2210, 10:40 PM

HW Helper
P: 1,361

If the sample size is only 5 i would be hesitant to do any confidence interval but, if pushed, if sigma were known, and if told that the data were known to be normally distributed, the Zinterval would be appropriate.



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