# Different results when calculating confidence interval

I'm trying to replicate the results from a paper which states: "Estimated overall accuracy is 79.6% with a standard error of 5.1% which would yield a 95% confidence interval of 69.5% to 89.7%.".

When I calculate the 95% confidence interval using the 5.1% standard error, I gain a CI of 10% not 10.1% as I presume it is in the paper. As a result my CI range is 69.6% - 89.6%, whereas in the paper it is 69.5% - 89.7%

Where am I going wrong?

Using R...

round(5.1*1.96,2)
10
79.6 - 10
89.6
79.6 + 10
69.6

• The difference is 0.1, they probably used the real accuracy with many decimals to calculate the CI and then rounded it. Aug 5 at 10:28
• Given that the implicit multiplier of $2$ in this calculation $2\%$ greater than the value of $1.96$ it is approximating, you shouldn't be fussing over a deviation of just $0.1/10 = 1\%$!
– whuber
Aug 5 at 13:33