Here is the full question.
In order for a vaccine to be effective, it should reduce a person's chance of acquiring a disease. Consider a hypothetical vaccine for malaria‚- a tropical disease that kills between 1.5 and 2.7 million people every year.1 Suppose the vaccine is tested with 700 volunteers in a village who are malaria-free at the beginning of the trial. Three hundred of the volunteers will get the experimental vaccine and the rest will not be vaccinated. Suppose that the chance of contracting malaria is 10% for those who are not vaccinated.
Construct a two-way table to show the results of the experiments if:
(a) The vaccine has no effect
(b) The vaccine cuts the risk of contracting malaria in half
Answer:
Step-by-step explanation:
From the given information above:
Suppose, there is no effect from the vaccine, the risk of having malaria for vaccine & no vaccine is equal to 0.1
Now, the Probability of not having malaria if vaccinated or no vaccinated = 1 - 0.1 = 0.9
Therefore: the table is shown below as follows:
Malaria No Malaria Total
Vaccinated 300 × 0.1 = 30 300 × 0.9 = 270 300
No Vaccine 400 × 0.1 = 40 400 × 0.9 = 360 700-300 = 400
Total 40 + 30 = 70 270 + 360 = 630 700
(b)
The risk of malaria for vaccinated if the vaccine cuts the risk of contracting malaria in half are equal to 0.1/2 = 0.05
Thus; the probability of not getting malaria if vaccinated = 1 - 0.05 = 0.95
The table can then be computed as follows:
Malaria No Malaria Total
Vaccinated 300 × 0.05 = 15 300 × 0.95 = 285 300
No Vaccine 400 × 0.1 = 40 400 × 0.9 = 360 700-300 = 400
Total 40 + 15 = 55 285 + 360 = 645 700
