Question

In a large clinical​ trial, 398 comma 820 children were randomly assigned to two groups. The treatment group consisted of 198 comma 082 children given a vaccine for a certain​ disease, and 26 of those children developed the disease. The other 200 comma 738 children were given a​ placebo, and 78 of those children developed the disease. Consider the vaccine treatment group to be the first sample. Identify the values of n 1​, ModifyingAbove p with caret 1​, ModifyingAbove q with caret 1​, n 2​, ModifyingAbove p with caret 2​, ModifyingAbove q with caret 2​, p overbar​, and q overbar.

Answer 1

See explanation

Explanation:

Given:

398,820 were randomly assigned to 2 groups

198,082 were given a vaccine and 26 developed the disease

200,738 were given placebo and 78 developed the disease

For the vaccine treatment group:

Given:

Sample size, n₁ = 198,082

X₁ = 26

p'₁ = X₁/n₁
`= (26)/(198082) = 0.000131`

q'₁ = 1 - p'₁ = 1 - 0.0001312 = 0.99986

For Placebo treatment group:

Sample size, n₂ = 200,738

X₂ = 78

p'₂ = X₁/n₁
`= (78)/(200738) = 0.0003886`

q'₂ = 1 - p'₂ = 1 - 0.0003886 = 0.99961

`Over P = (n_1p_1 + n_2p_2)/(n_1 + n_2) = ((198082*0.0001312) + (200738*0.0003886))/(198082 + 200738)`

`= (25.988 + 78.007)/(398820)`

`= 0.0002608`

`Over q = 1 - overp = 1 - 0.0002608 = 0.9997`