1. Government standards limit the airborne amount of a known cancer causing gas. A company using a known cancer causing gas in its production process limits the exposure of its employees to the gas by shutting down production when the amount of the gas reaches 3 ppm with a standard deviation of 0.5 ppm.
a. (2) If you are the plant manager and you are told management wants as little down time as possible, would you choose a larger or a smaller value of alpha to test whether the amount of gas is dangerous? Explain.
b. (2) If you were an employee in the plant, would you want the choice of alpha to be larger or smaller? Explain.
c. (5) A random sample of 50 air specimens from various sensors in the plant produced a mean of 3.1 ppm. Is this sample data sufficient to shut down production? Use alpha = 0.01.
d. (2) Describe both Type I and Type II errors in the context of this problem.
e. (6) Calculate the probability of Type II error if in fact the true mean plant level if 3.1 ppm. Use alpha = 0.01.
f. (1) What is the value of the Power of the test in this case?
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