A toothpaste manufacturer wants to determine whether the addition of a certain chemical to their toothpaste will increase its ability to fight tooth...

A toothpaste manufacturer wants to determine whether the addition of a certain chemical to their toothpaste will increase its ability to fight tooth decay. A group of 100 people are chosen and an experiment is conducted. Of the 100 people using the toothpaste with the chemical addition for a specified period of time, the manufacturer finds that they have an average of 8 cavities and a standard deviation of 3 cavities. It turns out that the sample standard deviation correctly estimates the population standard deviation. The average number of cavities of people using the toothpaste without the chemical addition is known to be 9, based on a long term study that the company performed a couple of years ago. Can we conclude at the 1% level of significance that the addition of the chemical made a difference the toothpaste's ability to fight tooth decay? Perform an appropriate hypothesis test with all of the necessary steps.