An advertising agency that serves a major radio station would like to estimate the average amount of time that the station’s audience spends listening to radio on a daily basis. What sample size is needed if the agency wants to be 90% confident of being correct to within +/- 5 minutes? From past studies, the standard deviation is estimated at 45 minutes.
I do not even know how to start. Any hit will be appreciate!
Assume that the distribution is normal.
Let $\sigma$ your standard deviation, $n$ the sample size, and $\mathrm{ME}$ your (semi-)margin of error. Then you just need $$ z_{95\%} \frac{\sigma}{\sqrt{n}} \le \mathrm{ME}. $$ Therefore $$ N\ge \left\lceil \left(\frac{z_{95\%} \sigma}{\mathrm{ME}}\right)^2\right\rceil $$