4. [FINA2230 Final Exam 2020] A health care official tests the viral filtration efficiency (VFE) of three brands of surgical masks. 7 masks from each brand are sampled and their corresponding filter quality factor (q, in unit of 1 mm-1 H,O) are tabulated as follows: Brand A: 0.263, 0.301, 0.420, 0.316, 0.351, 0.288, 0.437 Brand B: 0.365, 0.372, 0.246, 0.337, 0.289, 0.431, 0.363 Brand C: 0.320, 0.391, 0.358, 0.402, 0.371, 0.396, 0.417 Assume that the filter quality factors of the three populations are normally distributed, with the same variance. (a) Compute the F test statistic for testing the hypothesis that the three brands have the same efficiency against the alternative that two of the brands have different efficiencies. Find the p-value of the test. (b) Give the MME of the common standard deviation of the three populations. 5. Consider the density f (x; b) =(b+ 1)bx(1 -x)b-1 for 0 0. The test Ho: b = 1 against H1: b = 2 is conducted based on a sample of size 2. (a) Derive the most powerful test. An experimenter collects a sample with x1 = 0.51 and x2 = 0.40. (b) Find the p-value of the test for the sample. Should H, be rejected at a= 0.1? 6. For a Po( O) population, you test Ho: 0= 5 against H1: 0# 5 using the test statistic 3X =X + X, + X . To construct a test with an approximate level of significance of 7%, an experimenter sets the critical region {3X Q. Draw a graph of h(x) = |x - & |- |x - al. Consider the density f (x; 0) =0.5exp(-| x- 0)) for x ER and O E R. The test Ho: 0= 6 against H,: 0