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 Practice Problems These come from Dan Teague. The Question: Suppose a dentist wants to know if a daily dose of 500 mg of vitamin C will result in fewer canker sores in the mouth than taking no vitamin C. Consider four scenarios. 1. The dentist, working though the local dental society, convinces all of the dental patients in town with appointments in the first two weeks in December to be subjects of a study. He divides them into two groups, those who take at least 500 mg of vitamin C each day and those who do not. He asks them how often they have canker sores in their mouths and checks their dental record to see who has complained of canker sores. He compares the proportion of those who take vitamin C and complain about canker sores with the proportion of those who don’t take vitamin C daily and complain of canker sores. There is a significantly difference in the two proportions, with a significantly smaller proportion of those taking vitamin C having canker sores. What can we conclude? 2. The dentist, working though the local dental society, convinces all of the dental patients in town with appointments in the first two weeks in December to be subjects of a study. He randomly assigns half of them to take 500 mg of vitamin C each day and half to abstain from taking Vitamin C for three months. At the end of this time he determines the proportion of each group that has suffered from canker sores during those three months. There is a significant difference in the two proportions, with a significantly smaller proportion of those taking vitamin C having canker sores. What can we conclude? 3 The dentist, working though the local dental society, selects a random sample of the dental patients in town and convinces them to be subjects of a study. He divides them into two groups, those who take at least 500 mg of vitamin C each day and those who do not. Then he asks them how often they have canker sores in their mouths and then checks their dental record to see who has complained of canker sores. He comparers the proportion of those who take vitamin C and complain of canker sores with the proportion of those who do not take vitamin C and complain of canker sores. There is a significantly difference in the two proportions, with a significantly smaller proportion of those taking vitamin C having canker sores. What can we conclude? 4. The dentist, working though the local dental society, selects a random sample of dental patients in town and convinces them to be subjects of a study. He randomly assigns half of them to take 500 mg of vitamin C daily for three months. At the end of this time he determine that proportion of each group that has suffered canker sores during those thee month. There is a significant difference in the two proportions with a significantly smaller proportion of those taking vitamin C having canker sores. What can we conclude?