1. (i) The weights of the eggs produced by a farmer's hens have a standard deviation of 9g. He feeds some hens a vitamin supplement that will be cost-effective if the average egg weight increases by at least 3.5g. He obtains 16 eggs from the vitamin-fed hens that have an average weight 4.5g larger than the eggs from the hens that have not received extra vitamin. Can the farmer conclude that the increase is significant and that he can start feeding all his hens with the supplement? [1.5p]