An official of the Iowa Department of Highways wants to compare the useful life, in months, of two brands of paint used for striping roads. The mean number of months Cooper Paint lasted was 36.2 with a standard deviation of 1.114 months. The official review 35 road stripes. For King Paint, the mean number of months was 37.0 with a standard deviation of 1.3 months. The official reviewed 40 road stripes. At the .01 significance level is there a difference in the useful life of the two paints? Compute the p-value.
x-bar1=36.2, sigma1=1.114 n1=35
x-bar2=37.0 sigma2=1.3 n2=40
standard error=(sigma1^2 /n1+sigma2^2/n2)^0.5