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 (λ) random variable X with expected value E[X] = 1/λ = (200/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 the number N of chips that fail in one day, design a significance test for the null hypothesis test H0 that 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.
(b) How many chips must be tested so that the significance level is α = 0.01.
(c) If we raise the temperature of the test, does the number of chips we need to test increase or decrease?