Question: Let \(X\) be a random variable that represents assembly time for Ford Taurus. The Wall Street Journal reported that the average assembly time is \(\mu \) = 38 hours. A modification to the assemble procedure has been made. Experience with this new method indicates that \(\sigma \) = 1.2 hours. It is thought that the average assemble time may be reduced by modification. A random sample of 47 new Ford Taurus automobiles coming off the assembly line showed the average assemble time using the new method to be \(\bar{X}\) = 37.5 hours. Does this indicate that the average assemble time has been reduced? Use \(\alpha \) =0.01.