A study was initiated to investigate the effect of two drugs, administered simul

Question

A study was initiated to investigate the effect of two drugs, administered simultaneously, on reducing human blood pressure. It was decided to use three levels of each drug and to include all nine combinations in the experiment. Nine high-blood-pressure patients were selected for the experiment, and one was randomly assigned to each of the nine drug combinations. The response observed was a drop in blood pressure over a fixed interval of time. Now Suppose that a balanced completely randomized design is to be employed and that prior experimentation suggests that sigma = 20.

a) How many replications would be required to estimate any treatment (drug combination) mean correct to within plus or minus 10 with probability .95?

Explanation / Answer

a)

let S be the sample mean and N be the no. of replications required.

(S) which is standard deviation of sample mean = (20)/N

z = [S - (S)]/(S)

given

p(-10 < S - (S) < 10 ) = 0.95

=> p(-10 < z(S) < 10) = 0.95

=> p( -10 < z(20)/N < 10) = 0.95

=> p( -N/2 < z < N/2) = 0.95

=> (N/2) - (1 - (N/2)) = 0.95

=> 2(N/2) - 1 = 0.95

=> (N/2) = 1.95/2 = 0.975

using normal table , we have

N/2 = 1.96

N = 15.36 15

hence we need 15 replications

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