Question: Dr Arnold Schwarzenegger, a local traffic engineer with the Municipality of Anchorage (MOA) wants to compare the useful life of two brands of paint used for roadway striping. The mean number of months that the Ralph Lauren paint lasted was \(46.86\) months with a standard deviation of 11.76 months. The random sample size for Ralph Lauren Paints was 9. Whereas, the DuPont paint roadway striping's lasted 50.98 months with a standard deviation of 20.64 months. The random sample size for the DuPont paint was 7. At a five percent significance level test the claim that the DuPont painted roadway striping's last longer than the Ralph Lauren painted roadway striping's. Assume the population standard deviations are unknown.