Question

A prospective purchaser wishes to estimate the mean dollar amount of sales per customer at a toy store located at an airlines terminal. Based on data from other similar airports, the standard deviation of such sales amount is estimated to be about $3.20.

 What size of random sample should she collect, as a minimum, if she wants to estimate

 the mean sales amount within $1.00 and with 99 percent confidence?

Answer 1

The critical value for $\alpha=0.01$ is $z_c=z_{1-\alpha/2}=2.576.$ Then

$$z_c\times \dfrac{\sigma}{\sqrt{n}}\leq1$$

$$n\geq(z_c\times\sigma)^2$$

$$n\geq(2.576\times3.2)^2$$

$$n=68$$