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Answer:
Step-by-step explanation:
From the given information:
The number of children that were randomly allocated to each vaccination group; n₁ = 200,000
No of polio cases X₁ = 57
Now, in the vaccine group:
the proportion of polio cases is:
= 0.000285
The number of children that were randomly allocated to the placebo group, n₂ = 200,000
No of polio cases X₂ = 142
In the placebo group
the proportion of polio cases is:
Null and alternative hypothesis is computed as follows:
H₀: There is no difference in the proportions of polio cases between both groups.
H₁: There is a difference in the proportions of polio cases between both groups.
Let assume that the level of significance ∝ = 0.05
The test statistic can be computed as:
Z = - 6.03
P-value = 2P(Z < -6.03)
From the Z - tables
P-value = 2 × 0.0000
= 0.000
We reject the H₀ provided that P-value is very less.
Therefore, we may conclude that there is a difference in the proportions of polio cases between the vaccine group and placebo group not due to chance.