Question

**Scenario 2: Air pollution ~** A chemical plant is
required to maintain sulfur dioxide levels in the working
environment atmosphere at an average level of no more than 0.125
parts per million (ppm). Safety engineers measure the levels at a
randomly chosen 10 intervals each week. If the sample mean sulfur
dioxide level is more than 0.15 ppm, the safety protocols say that
the plant will be evacuated while the air is scrubbed and machines
are adjusted. The standard deviation of the measurements is known
to be 0.04 ppm, and the testing scenario tests the hypotheses
H0:μ=0.125H_0:\mu=0.125H0:μ=0.125 vs
Ha:μ>0.125H_a:\mu>0.125Ha:μ>0.125.

Using the decision rule in the prompt above, what is the chance the safety engineers will make a Type I error? Submit your answer rounded out to four decimals.

Using the same decision rule, what is the power of this test if the mean pollution level is truly 0.14 ppm? Submit your answer rounded out to four decimal places.

Answer #1

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