I need only part D 4. 120 total points/ (public health) In one of the largest an
ID: 3297170 • Letter: I
Question
I need only part D
4. 120 total points/ (public health) In one of the largest and most famous human experiments ever conducted,n 1954 a randomized controlled trial was run to see whether a vaccine developed by a doctor named Jonas Salk was effective in preventing paralytic polio. A total of 401,974 children chosen to be representative of those who might be susceptible to the disease, were randomized to two groups: 200,745 children (the control group C) were injected with a harmless saline solution and the other 201,229 children (the treatment group T) were injected with Salk's vaccine.Explanation / Answer
Solution
Back-up Theory
The sample proportion, cap is the estimate of the population proportion, . Then, 99.9% confidence interval for is given by:
cap ± Z0.0005 x sqrt{ cap(1 – cap)/n }, where Z0.0005 = upper 0.05% point of N(0, 1) and n is the sample size.
Now, to work out the solution,
The left edge of the 99.9% confidence interval for Tcap = Tcap - Z0.0005 x sqrt{Tcap(1 – Tcap)/n} and we want this to be just positive. i.e.,
Tcap - Z0.0005 x sqrt{Tcap(1 – Tcap)/n } > 0. This, in turn implies,
n > {Tcap(1 – Tcap)}/{( Tcap/ Z0.0005)2}.
Now, using Excel Function on N(0, 1), Z0.0005 = 3.290527 and we are given Tcap = 0.0001640.
Substituting, n > 66010.92815. i.e., n = 66011
Similarly, substituting Ccap = 0.0005729, n > 32113.94. i.e., n = 32114
Thus. to ensure that the lower edge of the 99.9% confidence interval for Tcap and Ccap are just positive, the minimum sample size required are 66011 and 32114 respectively.
But, the question assumes that n is the same for both. Hence, the required sample size is 66011 for each or the total sample size is 132022 ANSWER
Clearly, the sample size used by the Designers of the study is unduly large.
The only plausible justification for this is that the Designers might have expected the incidence paralytic polio to be extremely low.
DONE