Question: A NAPA Auto Parts supplier wants information about how long car owners plan to keep their cars. A simple random sample of 25 car owners results in \(\bar{X}=7.01\) years and s = 3.74 years respectively. Assume that the sample is drawn from a normally distributed population and find the following:

a. The sample size, if you want to be 99% confident that the sample mean is within 0.25 years (or 3 months) of the population mean, assume that \({{\sigma }_{X}}\) = 3.74 (based on the latest result).

b. Now assume you want to be 95% confident that the sample mean is within 0.25 years of the population mean, under the same assumptions, what happens to the sample size and would you say that it is a better or less effective value?

c. Interpret your results.