Mathematics, 29.05.2020 17:00 priarm8799
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 second group. For ethical reasons, and because it was suspected that knowledge of the vaccine administration would effect subsequent diagnoses, the experiment was conducted in a double blind fashion. That is, 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
(a) Use a hypothesis-testing procedure to determine whether the proportion of children in the two groups who contracted paralytic polio is statistically different. Use a probability of a type I error equal to 0.05.
(b) Repeat part (a) using a probability of a type I error equal to 0.01.
(c) Compare your conclusions from parts (a) and (b) and explain why they are the same or different.
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