Let R₁ be a rejection region with significance level a for testing 

a. Show that the UIT is a level α test.

b. 

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H01:0₁ versus Hal: 02₁, and let R₂ be a level a rejec- tion region for testing Ho2:02 versus Ha2: 092, where ₁ and ₂ are two disjoint sets of possible values of 0. Now consider testing Ho: 0 2₁ U₂ versus the alternative Ha: 0 21 U 2₂. The pro- posed rejection region is R₁ R₂. That is, Ho is rejected only if both Hoi and Ho₂ can be rejected. This procedure is called a union-intersection test (UIT).