@Carl Love 

Hi,

thanks for the explanation. I did not take this into account as you have surely perceived.

I was not even aware of the fact that there could be a non-integer degree of freedom (it was burries deep in my subconsciousness and it popped up a little as you have mentioned it - but not really).

However, I tried to find the non-integer degrees of freedom and wiki does not mention it (or I overlooked it). I am quite sure that "in all of statistics" they do not mention it either (but not absolutely sure) - and as the name suggests: it includes everything belonging to statistics

How is it defined?

Thanks a lot for your help.

@Carl Love 

Hi,

sorry for being not so concise with my question.

I calculated a two tail t-test by hand. You can follow the procedure by executing the maple code above - first section. I hoped I can just post the maple sheet - but it was not attached. My resullt is

upper bound 1.5225682336585966
lower bound -3.122568233658591
for a 0.95 confidence interval.

For the cross check I simply typed:

TwoSampleTTest(a, b, 0, confidence = .95, summarize = embed)

The result is quite different. I thought maybe it is a two tail one tail issue and restricted the confidence interval to 0.975.

TwoSampleTTest(a, b, 0, confidence = .975, summarize = embed)

The result is close but the discrepancy is still too high. You may argue that my t-table table is not accurate enough but I also used a numerical recipes implementation to get them - not perfect but 5-6 digits should be accurate.

TwoSampleTTest(a, b, 0, confidence = .95, summarize = embed) should have done it - or I interpreted the function the wrong way. However, I would be glad if someone can tell me what I have done wrong.

Best regards,

Oliver