In the past, a car company had to face a burst of bad publicity when faulty brake parts led to car accidents. They would like to ensure their new car models do not have similar problems. To do so, company staff wants to test the strength of a certain component of the brakes. Previous work has determined the standard deviation is 2.5 psi. They would like a 99% confidence for their experiment and a margin of error of 0.5.
a) Find the sample size for the experiment.
b) Find the sample size for the experiment if they wanted a margin of error of 0.25.