# Thread: confidence error, confusing question

1. ## confidence error, confusing question

Hi The question is: In measuring the time people take to react to a flashing light, it is estimated from a large number of previous experiments that the standard deviation is 0.5 seconds. How many observations must be taken in a new experiment in order to be 99% confident that the error in the estimate of the mean reaction time will not exceed 0.1 seconds? The answer is 166 but im not quite sure how this is obtained, any ideas?

2. YUP, 166 is correct .The CI for a mean is...
$\displaystyle ( \bar x-z_{\alpha/2}\sigma/\sqrt{n} , \bar x+z_{\alpha/2}\sigma/\sqrt{n})$.

Now we want $\displaystyle z_{\alpha/2}\sigma/\sqrt{n}\le B$, where B is the bound on your error.

Solving for n we get $\displaystyle \biggl({z_{\alpha/2}\sigma\over B}\biggr)^2\le n$.

If you plug your constants into this, a lower bound for n is... 165.8944 and you should always round UP here.
And they did a good job by using 2.576 for the z percentile, which you can steal from a t table.