An advertisement for a toothpaste claims that employ of the product significantly reduces the number of cavities of children in their cavity-prone years. Cavities per year for this age group are normal with mean 3 and standard deviation 1. A study of 2500 children who used this toothpaste found an average of 2.95 cavities per child. Assume that the standard deviation of the number of cavities of a child using this new toothpaste remains equal to 1.
(a) Are these data strong enough, at the 5 percent level of significance, to establish the claim of the toothpaste advertisement?
(b) Is this a significant enough reason for your children to switch to this toothpaste?