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 and overfills the cans, the manufacturer takes a random sample of 81 cans. Assume the population standard deviation is 3.0 ounces, and the volume of paint in the cans is normally distributed. Assume that, unknown to the researcher, the true mean volume of the cans is 129 ounces. a) What are the null and alternative hypotheses? b) For what values of should Ho be rejected so that the power of the test is 0.95? What will the level then be? c) How large of a sample is needed so that a 1% level test has power 0.95?
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 and overfills the cans, the manufacturer takes a random
sample of 81 cans. Assume the population standard deviation is 3.0 ounces, and the volume
of paint in the cans is
mean volume of the cans is 129 ounces.
a) What are the null and alternative hypotheses?
b) For what values of should Ho be rejected so that the power of the test is 0.95?
What will the level then be?
c) How large of a sample is needed so that a 1% level test has power 0.95?
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