Let H0 and H1 be simple and let α ∈ (0, 1). Suppose that T∗ is a UMP test of size α for testing H0 versus H1 and that β < 1,="" where="" β="" is="" the="" power="" of="">∗ when H1 is true. Show that 1 - T∗ is a UMP test of size 1 - β for testing H1 versus H0.