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and Probability of Type II Error 613 cid (in dpm, and for dent 2 and 3 1 . a ) X- 50 7 2.33 x- $5 10 / 10 = 2 normedf ( 2, 1000 . 0 , 1 ) = 6. Optical fibers are used in telecommunications to transmit light. Suppose current technology allows production of fibers that b) 1 transmit light about 50 km. Researchers are trying to develop a new type of glass fiber that will increase this distance. In evaluating a new fiber, it is of interest to test Ho: | = 50 versus Ha: M > 50, with u denoting the mean transmission distance for the new optical fiber. a) Assuming o = 10 and n = 10, what is the power of the test when u = 55? Use a = .05. b) What is the probability of a Type II error in this test? c) If n = 100, and the other information from part a was the same, would the power of the test increase or decrease? Explain. d) If u = 65, and the other information from part a was the same, would the power of the test increase or decrease? Explain. e) If a = .01, and the other information from part a was the same, would the power of the test increase or decrease? Explain. 50 -50 10 = - 1:58/19 - HA 0. 0 8 7 0 5) Not reject 50- 55 = 5 close to o Vroo 2 It would 50 - 65 = - 4. 74 342 =