HW12

STAT 5102 HW12 Answer p. 596, Q9 and p. 632 Q4, p. 633 Q8 from the textbook, and the following additional questions. Question 1 (calculating p-value): Calculate the p-value of the testing problem in Q3 on page 596 of the textbook, using the data in Q2. (Hint: use the formula in Q9). Additional Question 2 (p-value for the large-sample likelihood ratio test for comparing Poisson samples): Let X 1 , · · · , X m ∼ Poisson( λ ), Y 1 , · · · , Y n ∼ Poisson( μ ), and X 1 , · · · , X m , Y 1 , · · · , Y n be jointly independent. Consider the testing problem H 0 : λ = μ against H 1 : λ ∕ = μ. In HW11 (Additional Question 1), you have derived the test statistic for the likelihood ratio test and limiting distribution based on the Wilk’s theorem. Now, assume that m = 20, n = 30, and the observed values for ¯ X = 1 m ஀? m i =1 X i and ¯ Y = 1 n ஀? n j =1 Y j are 1 and 1 . 5, respectively. (a) Calculate the approximate p-value. (b) Based on the p-value, do we reject H 0 at the level 0 . 05? Do we reject H 0 at the level 0 . 01? Please submit answers for the 5 questions listed above. Practice problems listed below are optional but useful for understanding the chi-squared test and exam preparation. Additional practice questions p. 633 Q9 (a) p. 646 Q5 and Q9 from the textbook.