Parents of teenage boys often complain that auto insurance costs more, on average, for teenage boys than for teenage girls. A group of concerned parents examines a random sample of insurance bills. The mean annual cost for 36 teenage boys was \($679.\) For 23 teenage girls, it was \($559.\) From past years, it is known that the population standard deviation for each group is \($180.\) Determine whether or not you believe that the mean cost for auto insurance for teenage boys is greater than that for teenage girls.