Question

Two groups, A and B, of arthritis sufferers are given a placebo and a prescription drug respectively for a period of one month. Then, the time in seconds taken to walk 10 yards is measured.

The measured times in the two groups are A[1], ... ,A[m] and B[1] , ... , B[n] .

It is required to test the hypothesis H[0] : mu=nu  where mu and nu denote respectively the mean walking times in the (hypothetical) populations of sufferers treated with the placebo and prescription drug respectively.

Express the data in linear model form Y[i] = Beta[0] + x[i]Beta[1] + e

; i = 1, ... , m + n;

in such a manner that the hypothesis H[0] : mu = nu is equivalent to the hypothesis H[0] : Beta[1] = 0: Express clearly Beta[0] and Beta[1] in terms of mu and nu and express Y[1], .... , Y[m+n] in terms of the A[i] and B[i]. Also give the numerical values of x[1], ... , x[m+n].

Answer 1