1. 100,000 Massachusetts adults were randomly sampled with twofactors recorded: whether or not the individual
had diabetes, and whether or not the person ate Kale. Thefollowing gives a table of the results.
Diabetes No Diabetes
Kale: 796 9187
No Kale: 9900 80117
(a) We write p(Diabetes | Kale) for the probability that aMassachusetts adult who eats kale has diabetes.
Either give a value for p(Diabetes | Kale) or explain why itcannot be computed.
(b) We write ^p(Diabetes | Kale) for the proportion ofKale-eating members of our sample above that had
diabetes. Either give a value for ^p(Diabetes | Kale) or explainwhy it cannot be computed.
(c) Give 95% confidence intervals for the probability of havingdiabetes for both the kale-eating and non-kale-
eating members of our Massachusetts adults.
(d) Can you conclude that the kale-eaters are less likely tohave diabetes? Explain your reasoning.
(e) Can you conclude that kale consumption causes a lowerdiabetes rate in this population? Explain your
reasoning.
(f) Come up with a possible theory that explains why kale-eatershave a lower rate of diabetes, but does not
assume that kale causes the lower rate.
