A machine used for producing "quarter inch" rivets is to be checked by taking a random sample of 10 rivets and measuring their diameters. It is feared that the wear-off factor of the machinewill cause it to produce rivets with diameters less than 1/4 in. Describe the critical region in terms of X, the average of the 10 diameters, for a test of significance of 1%, of
H_0: mu= 0.25 versus H_1: mu = mu_1 < 0.25,
If it can be assumed that the diameters are distributed as N(mu, (0.0015)^2 for a wide range of values of mu. What is the power of the test at mu = 0.2490?