III 4- When 100 tacks were thrown on a table, 72 of them landed point up. Assuming independence, obtain a 95% confidence interval for the probability p that a tack of this type lands point up. : Obtain a best critical region of size .05 to test the null hypothesis Ho po against the alternative H₁: P1 <. Explain why the test is UMP. Determine the power of the test at p₁ =. In this case decide whether to accept or reject the null hypothesis. You may assume that sample is large enough that the normal ap- proximation can be used.