1. ## Confidence level

The director of a museum would like to know what fraction of the museum associates make purchases through the gift shop catalog

A) If no preliminary study is done, how large a sample must be taken if the director is to say with 90% confidence that the sample estimate is within 2% of the population proportion?

B) A preliminary study showed that out of 60 associates 12 have used the gift shop catalog, what size sample does the director need in order to say with 90% confidence that the sample estimate is within 2% of the population proportion??

Any guidance would be much appreciated, not exactly sure how to start with this one, thanks in advance for any help

2. A 90% confidence interval for p is $\displaystyle \hat{p} \pm z_{0.05} \sqrt { \frac {\hat{p}(1-\hat{p)}}{n}}$

So you want $\displaystyle z_{0.05} \sqrt { \frac {\hat{p}(1-\hat{p})}{n}} = 0.02$

You don't know $\displaystyle \hat{p}$ in part (A), (in part (B) $\displaystyle \hat{p}$ is 12/60) but you can use the fact that $\displaystyle \hat{p}(1-\hat{p}) \le \frac {1}{4}$

Now all you have to do is solve for n.