An agronomist hopes that a new fertilizer she has developed will enable grape growers to increase yield of each grapevine by more than 5 pounds. To test this fertilizer she applied it to 44 vines and used the traditional growing strategies on 47 other vines. The fertilized vines produced a mean of 58.4 pounds of grapes with standard deviation 3.7 pounds, while the infertilized vines yielded an average of 52.1 poounds with standard deviation 3.4 pounds of grapes. Do these experimental results confirm the agronomist's expectations?

Please explain your answer thoroughly and clearly. You should use a hypothesis test to solve this question.