[Q] Proper number of sig figs for 95% confidence intervals?

Hi,

Suppose I measure the weights of 12 pennies. I obtain a sample mean xbar = 2.5150, and standard deviation s = 0.0316. I then calculate the 95% confidence interval using the appropriate t value, and obtain CI = 0.0201. What is now the proper way to report these findings?

My textbook suggests (and a document I found online corroborates) that the result should be reported as 2.52(±0.02)g, because the standard error should always be rounded to 1 sig fig (unless the answer starts with 1, in which case you keep an extra). Then, the mean is rounded because the last digit of the value is the first digit of the error.

However, my friend’s stats class said the result should not be rounded to avoid losing precision, i.e. 2.5150(±0.0201)g. Our GSI says ‘usually’ you don’t round.

So I’m not sure who to believe or what’s typically accepted. To me it feels disingenuous to report extra digits when you’ve just admitted you’re uncertain of them.

Thanks,

submitted by /u/Plazmotech
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Nevin Manimala

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