This is a follow-up question to Question 4(a-c) in Homework 4. You don't have to correctly answer that question in order to solve this question. Suppose X1, ... , Xn Bernoulli(p) with unknown p. Consider testing for Ho : p= Po vs. H1 : p + po for some known quantity po E (0, 1). Based on Question 4(c) in Homework 4, an approximate (1 – a) x 100% CI for p (when n is large) is i.i.d. (ên + Za/2V Pn(1 – Pm) , Pn+ 21-a/2\ Pn(1 – Pn) 2013. where pn = X,n and z3 is the B-quantile for standard normal. Please construct a hypothesis test with type I error rate being approximately 0.05 when n is large. Instruction: In your answer, please specify your test (i.e., when do you reject Ho and when do you not reject Ho?), and justify that it indeed has type I error rate 0.05. In your justification, if you cite a theorem studied in class, please name that theorem or state the slide number and lecture note number that contains the theorem.

Question 4 Suppose that 1000 customers are surveyed and 850 are satisfied or very satisfied with a corporation's products and services. Test the hypothesis Ho : p = 0.9 against H1 : p + 0.9at a = 0.009. Find the P-value. Но- The P-value is less than (choose the least possible). Click if you would like to Show Work for this question: Open Show Work Ouestion A

If P(A) = 0.4, P(B) = 0.5, and P(AB) = 0.3, find (a) P(AUB), (b) P(An B'), and (c) P(A'U B').