Question: A state has just changed one of its toll roads from human collection of tolls to machine collection. The idea behind the change was to allow traffic to flow more smoothly through the toll plaza. With human attendants, the mean number of cars passing through the toll plaza was 1253 per hour. A random sample of 100 days under the new machine system of toll collections show a mean of 1261 cars passing per hour with a standard deviation of \(59\). Based on the following statistics, have the machines improved the flow of traffic through the toll plaza?