I'm a TA in stat for med students and when discussing confidence intervals together with the one-sample t-test, I got doubts on the decimals that should be retained. Specifically, we tested a data set of the body height of 3400 people against the null hypothesis of the average being equal to 170 cm. R gave a sample mean of 172.3974 with a confidence interval from 172.0846 to 172.7102. Sample SD was 9.8, the input heights were given in whole numbers.
A participant noted that giving seven significant figures would equal faking precision. I agree, but with such a narrow CI, should it really only be three like in the input data?
Random generation of 3400 body heights up to microns with the same mean and SD indicated that the first five significant figures of the upper and lower bound remained the same after cropping the four simulated decimals.
What's more, if both bounds of the interval rounded to the same integer, as could easily have been the case, the CI would be a single number.