In 2004, the state of North Carolina released to the public a large data set containing information on births recorded in this state. This data set has been of interest to medical researchers who are studying the relationship between habits and practices of expectant mothers and the birth of their children. The following histograms show the distributions of weight gain during pregnancy by 875 younger moms (less than 35 years old) and 139 mature moms (35 years old and over) who have been randomly sampled from this large data set. The average weight gain of younger moms is 30.36 pounds, with a standard deviation of 14.39 pounds, and the average weight gain of mature moms is 28.72 pounds, with a standard deviation of 13.64 pounds. Do these data provide strong evidence that there is a significant difference between the two population means? Conduct a hypothesis test.