A paint manufacturer fills cans of paint using a machine that has been calibrated to fill...

A paint manufacturer fills cans of paint using a machine that has been calibrated to fill the cans to contain an average of 1 gallon (128 ounces) each. To test whether their machine has come out of calibration, the manufacturer takes a random sample of 100 cans and finds that they average 128.2 ounces with a sample standard deviation of 4 ounces, and the volume of paint in the cans is normally distributed. Is this strong evidence that the can- filling machine is set too high? Carry out the appropriate hypothesis test at the α = 5% level.

e) Find the probability of a Type II error if, in fact, μ = 129. Suppose we can assume σ = 4.

f) What would happen to the probability of a Type II error if μ was even further away from the hypothesized value of 128?

g) What is the probability of a Type I error?

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orchestra answered 1 year ago

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