Brushing your teeth helps prevent cavities, doesn’t it? Consider the following data from a survey and subsequent dental exam of Italian 12-year-olds (“Influence of Occlusal Disorders, Food Intake and Oral Hygiene Habits on Dental Caries on Adolescents,” Dentistry 2016).

a. Test whether brushing frequency and the presence/absence of cavities are independent in the population of Italian 12-year-olds at the .05 significance level.

b. Discuss the results of part (a): what are some possible explanations for this potentially surprising finding?

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Brushing Freq. Never Once a day 2 times a day 3 times a day 4 times a day Cavities 11 24 99 107 42 No cavities 7 21 77 117 30