5.13 Car insurance savings. A market researcher wants to evaluate car insurance savings at a competing company. Based on past studies he is assuming that the standard deviation of savings is $100. He wants to collect data such that he can get a margin of error of no more than $10 at a 95% con???dence level. How large of a sample should he collect?
We will use Margin of error to get the sample size \[ \mathbf{M}=CL*\frac{\sigma}{\sqrt n} \] \[ \text{The sample size is :}\\ n=(CL*\frac{\sigma}{M})^2 \] \[ n=(1.64*\frac{100}{10})^2 \] \[ n=268.96\equiv 269 \] The sample size should be 269.