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8.2.1: Effectiveness of a vaccine
10,000 individuals are divided evenly into two groups. The treatment group is given a vaccine and the control group is given a placebo. 95 of the 5,000 individuals in the treatment group developed a disease. 120 of the 5,000 individuals in the control group developed a particular disease. The standard error estimate is ~ 0.0029. A research team wants to determine whether the vaccine is effective in decreasing the incidence of disease. Does sufficient evidence exist to conclude that the proportion of developing a disease in individuals given the vaccine is less than that of individuals given a placebo?
1) What is the proportion of individuals in the treatment group that developed the disease? Type as: #.###
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2) What is the proportion of individuals in the control group that developed the disease? Type as: #.###
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3) What is the z-score? Type as: #.###
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4) What is the p-value? Type as: #.###
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