(a) Show that the variance of the sample mean ???? of ???? observations from a stationary AR(1) process (1 − ????????)????̃???? = ???????? is given by var[????] ≃ ????2

????

????(1 − ????)2

(b) The yields from consecutive batches of a chemical process obtained under fairly uniform conditions of process control were shown to follow a stationary AR(1)

process(1 + 0.5????)????̃???? = ????????. A technical innovation is made at a given point in time leading to 85 data points with mean ????1 = 41.0 and residual variance ????2

????1 = 0.1012 before the innovation is made and 60 data points with ????2 = 43.5 and ????2

????2 = 0.0895 after the innovation. Is there any evidence that the innovation has improved (increased) the yield?