2. 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 machine will 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 1% significance test of H0: μ = 0.25 versus H1: μ < 0.25. Assume that the diameters are distributed as N(μ, (0.0015)2) for a wide range of values of μ. What is the power of the test at μ = 0.2490? Graph the power curve of the test.