(1 point) When a chip fabrication facility is operating normally, the lifetime of a microchip operated at temperature T, measured in degrees Celsius, is given by an exponential (2) random variable X with expected value E[X] = 1/2 = (100/T)2 years. Occasionally, the chip fabrication plant has contamination problems and the chips tend to fail much more rapidly. To test for contamination problems, each day m chips are subjected to a one-day test at T = 100 C. Based on N, the number of chips that fail in one day, design a significance test for the null hypothesis Ho: the plant is operating normally. (a) Suppose the rejection set of the test is R = {N >0}. Find the significance level of the test as a function of m, the number of chips tested. a(m) = (b) At temperature 50 degree Celsius, how many chips must be tested so that the significance level is a= 0.052 m = Note that m must be an integer. (c) If we raise the temperature during the test, the number of chips we need to test will Increase