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.

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Chrisnando Chrisnando · Answer 1 · 2020-07-17T04:41:28+02:00

Answer:

See explanation

Step-by-step 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 [tex] = \frac{26}{198082} = 0.000131 [/tex]

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 [tex] = \frac{78}{200738} = 0.0003886 [/tex]

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

[tex]Over P = \frac{n_1p_1 + n_2p_2}{n_1 + n_2} = \frac{(198082*0.0001312) + (200738*0.0003886)}{198082 + 200738}[/tex]

[tex] = \frac{25.988 + 78.007}{398820} [/tex]

[tex] = 0.0002608 [/tex]

[tex]Over q = 1 - overp = 1 - 0.0002608 = 0.9997[/tex]