The Salk polio vaccine experiment in 1954 focused on the effectiveness of the vaccine in combating paralytic polio. Because it was felt that without a control group of children there would be no sound basis for evaluating the efficacy of the Salk vaccine, the vaccine was administered to one group, and a placebo (visually identical to the vaccine but known to have no effect) was administered to a second group. For ethical reasons, and because it was suspected that knowledge of vaccine administration would affect subsequent diagnoses, the experiment was conducted in a double-blind fashion, i.e. neither the subjects nor the administrators knew who received the vaccine and who received the placebo. The actual data for this experiment are as follows: Placebo group: n = 201,299: 110 cases of polio observed Vaccine group: n = 200,745: 33 cases of polio observed Determine if the proportion of children in the two groups who contracted paralytic polio is statistically different. Use a probability of type I error equal to 0.05
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