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1. 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 signifieance test for the null hypothesis test $H_{0}$ that the plant is operating normally. a) Find an expression for the significance level of the test as a function of $m$, the total number of chips tested such that the null hypothesis is rejected for $N>0$ b) How many chips must be tested for a significance level of 0.01 c) If we increase the temperature at which we test, does the number of chips needed increase of decrease, why?

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