# Math Help - Confidence Interval Question

1. ## Confidence Interval Question

Hi,

I was hoping that someone could help me with the following question by showing me how to do it using confidence intervals. Although I've done it using the standard error, I want to know how to do it using confidence intervals, but I'm not sure how, as we are not given the sample mean (x bar).

Experience with workers in a certain industry indicates that the time required for a randomlyselected worker to complete a job is approximately normally distributed with a standarddeviation of 12 minutes. If the sample mean is calculated as an estimate of the mean of allworkers, what is the relative accuracy of a measure based on a sample of 64 workers comparedwith one based on a sample of 16 workers?

Thank you very much!

2. $n\;=\;\frac{z^{2}s^{2}}{d^{2}}\;\implies\;d\;=\;\f rac{s*z}{\sqrt{n}}$

Then $\frac{d_{16}}{d_{64}}\;=\;\frac{\frac{s*z}{\sqrt{1 6}}}{\frac{s*z}{\sqrt{64}}}\;=\;\frac{\sqrt{64}}{\ sqrt{16}}\;=\;\frac{8}{4}\;=\;2$