5.7 A random sample of 10 observations is drawn from a normal population with mean m and variance 1. Instead of a normal-theory test, the ordinary sign test is used for H0 :m ¼ 0,H1 :m > 0, with rejection region K 2 R for K  8.

(a) Plot the power curve using the exact distribution of K.

(b) Plot the power curve using the normal approximation to the distribution of K.

(c) Discuss how the power functions might help in the choice of an appropriate sample size for an experiment.