Question

n a large clinical​ trial, 396 comma 651 children were randomly assigned to two groups. The treatment group consisted of 198 comma 747 children given a vaccine for a certain​ disease, and 37 of those children developed the disease. The other 197 comma 904 children were given a​ placebo, and 111 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

I guess you want to find the relative frequencies:

In total, we have 396,651 children

in sample 1, we have 198,747 children, and of those, only 37 developed the disease.

This means that the vaccine is not effective in:

p = 37/198,747 = 0.00019

For the placebo, we have a sample of 197,904 children in total, and 111 of them developed the disease, then we have a probability of the placebo not being effective is:

p = 111/197,904 = 0.00056

So we can see that the difference is significant, meaning that the placebo is not effective in more than twice the cases where the vaccine is not effective.